LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


RECEIVED    BY    EXCHANGE 


Class 


ALTERNATING  CURRENT 


COMMUTATOR   MOTORS 


BY  A.  S.  M'ALLISTER 


ALTERNATING 
CURRENT  COMMUTATOR  MOTORS 


A  thesis  presented  to  the  University  Faculty  of  Cornell 
University  for  the  Degree  of  Doctor  of  Philosophy. 


BY 
A.  S.  M'ALLISTER 


JUNE,  1905 


OF  THE 

(    UNIVERSITY 

V  OF  / 

XC*L!FORN£X 

^^»^  i  .     .-^^-^~ 


CONTENTS. 
ALTERNATING  CURRENT  COMMUTATOR  MOTORS. 

PAGE. 

REPULSION  MOTOR 18 

REPULSION-SERIES  MOTOR 33 

PLAIN  SERIES  MOTOR 49 

INDUCTIVELY  COMPENSATED  SERIES  MOTOR 56 

CONDUCTIVELY  COMPENSATED  SERIES  MOTOR 57 

INDUCTION  SERIES  MOTOR 61 

COMPENSATED  SERIES  MOTOR  WITH  SHUNTED  FIELD  COIL 75 

APPENDIX 79 


173262 


Alternating  Current  Commutator  Motors. 
Repulsion  Motor. 


A.    S.    M 


Reprinted  from  The  Sibley  Journal  of  Engineering,  Oct.,  1904. 


,TV 

r       OF  / 


ALTERNATING  CURRENT  COMMUTATOR  MOTORS. 
REPULSION  MOTOR.* 

A.  s.  M'AUJSTER. 

In  dealing  with  the  phenomena  connected  with  the  operation 
of  alternating  current  motors  of  the  commutator  type,  it  must 
be  constantly  borne  in  mind  that  the  machine  possesses  simul- 
taneously the  electrical  characteristics  of  both  a  direct  current 
motor  and  a  stationary  alternating  current  transformer.  The 
statement  just  made  must  not  be  confused  with  a  somewhat  sim- 
ilar one  which  is  applicable  to  polyphase  induction  motors,  since 
only  with  regard  to  its  mechanical  characteristics  does  an  induc- 
duction  motor  resemble  a  shunt-wound  direct  current  machine, 
its  electrical  characteristics  being  equivalent  in  all  respects  to 
those  of  a  stationary  transformer. 

Before  discussing  the  performance  of  repulsion  motors,  it  is 
well  to  investigate  a  few  of  the  properties  common  to  all  com- 
mutator type,  alternating  current  machines.  It  will  be  recalled 
that  when  current  flows  through  the  armature  of  a  direct  cur- 
rent machine,  magnetism  is  produced  by  the  ampere  turns  of 
the  armature  current,  such  magnetism  tending  to  distort  the 
flux  from  the  field  poles.  In  the  familiar  representation  of  the 
magnetic  circuit  of  machines, — the  two  pole  model, — the  arma- 
ture magnetism  is  at  right  angles  to  the  field  magnetism,  the 
armature  current  producing  magnetic  poles  in  line  with  the 
brushes.  The  amount  of  this  magnetism  depends  directly  on 
the  value  of  the  armature  current  and  the  permeability  of  the 
magnetic  path.  When  alternating  current  is  used,  the  change 
of  the  magnetism  with  the  periodic  change  in  the  current  pro- 
duces an  alternating  e.m.f.  which  being  proportional  to  the  rate 
of  change  of  the  magnetism  will  be  in  time- quadrature  to  the 
current.  The  armature  winding  thus  acts  in  all  respects  simi- 
larly to  an  induction  coil. 

It  is  not  essential  that  the  current  to  produce  the  alternating 
flux  flow  through  the  armature  coils  in  order  that  the  alter- 
nating e.m.f.  be  developed  at  the  commutator.  Under  whatso- 
ever conditions  the  armature  conductors  be  subject  to  changing 
flux  a  corresponding  e.m.f.  will  be  generated,  in  mechanical  line 

*  Abstract  of  thesis  for  Ph.D.  degree,  Cornell  University. 


Repulsion  Motor.  19 

with  the  flux  and  in  time- quadrature  to  it.  Referring  to  Fig.  i 
which  represents  a  direct  current  armature  situated  in  an  alter- 
nating field,  having  two  pair  of  brushes,  one  in  mechanical  line 
with  the  alternating  flux  and  one  in  mechanical  quadrature 
thereto.  When  the  armature  is  stationary  an  e.m.f.  will  be 
generated  at  the  brushes  A  and  A  due  to  the  transformer  action 
of  the  flux,  but  no  measurable  e,m.f.  will  exist  between  B  and 
B.  As  seen  above,  this  e.m.f.  is  in  time- quadrature  with  the 
field  (transformer)  flux  and  as  will  be  seen  later,  its  value  is  un- 
altered by  any  motion  of  the  armature.  At  any  speed  of  the 
armature,  there  will  be  generated  at  the  brushes  B  and  B  an 
e.m.f.  proportional  to  the  speed  and  to  the  field  magnetism  and 
in  time-phase  with  the  magnetism.  At  a  certain  speed  this 
"  dynamo  "  e.m.f.  will  be  equal  in  effective  value  to  the  "  trans- 
former "  e.m.f.  at  A  and  A,  though  it  will  be  in  time-quadra- 
ture to  it.  This  critical  speed  will  hereafter  be  referred  to  as 
the  "  synchronous  "  speed,  and  with  the  two-pole  model  shown 
in  Fig.  i ,  it  is  characterized  by  the  fact  that  in  whatsoever  posi- 


F/G.1-  ELECTROMOTWE  FORCES  PRODUCED . 
M    M*  ALTER  MATING  FIELD. 


2O  The  Sibley  Journal  of  Engineering. 

tion  on  the  armature  a  pair  of  brushes  be  placed  across  a  diam- 
eter, the  e.m.f.  between  the  two  brushes  will  be  the  same  and 
will  have  a  relative  time-phase  position  corresponding  to  the 
mechanical  position  of  the  brushes  on  the  commutator. 

A  little  consideration  will  show  that  the  individual  coils  in 
which  the  maximum  e.m.f.  is  generated  by  transformer  action 
are  situated  upon  the  armature  core  under  brushes  B  or  B,  al- 
though the  difference  of  potential  between  the  brushes  B  and  B 
is  at  all  times  of  zero  value  as  concerns  the  transformer  action. 
A  similar  study  leads  to  the  conclusion  that  the  e.m.f.  generated 
by  dynamo  speed  action  appears  as  a  maximum  for  a  single  coil 
when  the  coil  is  under  brush  A  or  A.  Assuming  as  zero  posi- 
tion, the  place  under  brush  A  and  that  at  synchronous  speed  the 
e.m.f.  generated  in  a  coil  at  this  position  is  e.  Then  the  e.m.f. 
in  a  coil  at  b  will  equal  e  also.  A  coil  a  degrees  from  this  posi- 
tion will  have  generated  in  it  a  speed  e.m.f.  of  e  cos  a  and  a 
transformer  e.m.f.  of  e  cos  (a±  90)  =^=  q=  e  sin  a.  Since  these 
two  component  e.m.f.s  are  in  time  quadrature  the  resultant  will 
be  V=  N/  (>cosa)2  +  (±  e  sin  a)'2  =  e  and  is  the  same  for  all  values 
of  a.  The  time-phase  position  of  the  resultant,  however,  will 
vary  directly  with  a  or  with  the  mechanical  position  of  the  coil. 
From  these  facts  it  is  seen  that  at  synchronous  speed  the  effective 
value  of  the  e.m.f.  generated  per  coil  at  all  positions  is  the  same 
and  that  there  is  no  neutral  e.m.f.  position  on  the  commutator. 

In  a  repulsion  motor  as  commercially  constructed,  the  secondary 
consists  of  a  direct  current  armature  upon  the  commutator  of 
which  brushes  are  placed  in  positions  1 80  electrical  degrees  apart 
and  directly  short  circuted  upon  themselves,  as  shown  in  the 
two-pole  model  of  Fig.  2.  The  stationary  primary  member  con- 
sists of  a  ring  core  containing  slots  more  or  less  uniformly 
spaced  around  the  air-gap.  In  these  slots  are  placed  coils  so 
connected  that  when  current  flows  in  them  definite  magnetic 
poles  will  be  produced  upon  the  field  core.  The  brushes  on  the 
commutator  are  given  a  location  some  15  degrees  from  the  line 
of  polarization  of  the  primary  magnetism,  or  more  properly  ex- 
pressed, the  brushes  are  placed  about  15  degrees  from  the  true 
transformer  position.  That  component  of  the  magnetism  which  is 
in  line  with  the  brushes  produces  current  in  the  secondary  by  trans- 
former action,  and  this  current  gives  a  torque  to  the  rotor  due 
to  the  presence  of  the  other  component  of  magnetism  in  me- 
chanical quadrature  to  the  secondary  current. 


Repulsion  Motor. 


21 


It  is  possible  to  make  certain  assumptions  as  to  the  relative 
values  of  the  magnetism  in  mechanical  line  with,  and  in  me- 
chanical quadrature  to  the  brush  line  and  thus  to  derive  the 
fundamental  equations  of  the  machine.  It  is  believed,  how- 
ever, that  the  facts  can  be  more  clearly  presented  and  the  treat- 
ment simplified  without  sacrifice  of  accuracy  if  the  assumption 
be  made  that  the  primary  coil  is  wound  in  two  parts,  one  in  me- 
chanical line  and  the  other  in  mechanical  quadrature  with  the 
axial  brush  position  as  shown  in  Fig.  2.  It  will  be  noted  that 
the  two  fields  produced  by  the  sections  of  the  primary  coil  if 


F/G.&*  -  TWf)-  POLE  MODEL  or  IDEAL  REPULSION  MOTOR. 

there  were  no  disturbing  influence  present,  would  have  a  result- 
ant position  relative  to  the  brush  line  depending  upon  the  ratio 
of  the  strengths  of  the  two  magnetisms.  The  angle  which  the 
resultant  field  would  assume  can  be  represented  by  /8  having  a 

value  such  that  cotan  (3  =  4  where  <£t  is  the  flux  through  trans- 

9r 
former  coil  and  <£f  is  flux  through  field  coil.     If  n  be  the  ratio  of 

turns  on  the  transformer  poles  to  those  on  the  field  poles,  then  for 
any  value  of  current  in  these  coils  (no  secondary  current) 


-7  =  n  or  n  =  cotan 


(i) 


22  The  Sibley  Journal  of  Engineering. 

It  is  understood  that  in  Fig.  2,  the  core  material  is  considered 
to  be  continuous  and  that  in  the  two-pole  model  represented 
both  field  poles  and  both  transformer  poles  are  supposed  to  be 
properly  wound. 

In  Fig.  2,  let  it  be  assumed  that  the  machine  is  stationary  and 
that  a  certain  e.m.f. ,  £,  is  impressed  upon  the  primary  circuits, 
the  secondary  being  on  short  circuit.  The  flux  which  the 
primary  current  tends  to  produce  in  the  transformer  pole  pro- 
duces by  its  rate  of  change  an  e.m,f.  in  the  secondary,  and  this 
e.m.f.  causes  opposing  current  to  flow  in  the  closed  secondary 
circuit.  If  the  transformer  action  is  perfect  and  the  transformer 
coil  and  armature  circuits  are  without  resistance  and  local  leak- 
age reactance,  then  the  magnetomotive  force  of  the  armature 
current  equals  that  of  the  current  in  the  transformer  coil,  and 
the  resultant  impedance  effect  of  the  two  circuits  is  of  zero 
value,  so  that  the  full  primary  e.m.f.,  £,  is  impressed  upon  the 
field  coil,  that  is  to  say,  with  armature  stationary  £t  =  O,  and 
E,-E. 

It  remains  now  to  investigate  the  effect  of  speed  on  the 
electromotive  forces  of  the  transformer  and  field  coils.  Assume 
a  certain  flux  3>f  in  the  field  coil.  At  speed  ,5  the  armature  con- 
ductors will  cut  this  flux  and  at  each  instant  there  will  be  gen- 
erated an  e.m.f.  therein  proportional  to  S<f>v  and  therefore,  in 
time-phase  with  the  flux.  This  e.m.f.  would  tend  to  cause  cur- 
rent to  flow  in  the  closed  armature  circuit,  which  current  would 
produce  magnetism  in  line  with  the  brushes,  and,  since  the 
armature  circuit  has  zero  impedance,  (assumed)  the  flux  so  pro- 
duced will  be  of  a  value  such  that  its  rate  of  change  through  the 
armature  coils  just  equals  the  e.m.f.  generated  therein  by  speed 
action.  At  synchronous  speed,  the  secondary  being  closed,  the 
flux  in  line  with  the  brushes  must  equal  that  in  line  with  the 
field  poles,  since  the  e.m.f.  generated  by  the  rate  of  change  of 
the  flux  in  the  direction  of  the  brushes  must  equal  that  gene- 
rated at  the  brushes  due  to  cutting  the  field  magnetism,  and  at  a 
speed  which  has  been  termed  synchronous  these  two  fluxes  are 
equal,  as  previously  discussed.  At  this  speed  the  two  fluxes 
are  equal  but  they  are  in  time- quadrature  one  to  the  other.  At 
other  speeds  the  two  fluxes  retain  the  quadrature  time-phase 
position,  but  the  ratio  of  the  effective  values  of  the  two  fluxes 
varies  directly  with  the  speed. 

Giving  to  synchronous  speed  a  value  of  unity,  at  any  speed, 


Repulsion  Motor.  23 

S,  the  transformer  flux  may  be  expressed  by  the  equation 

*t  =  S4>t  (2) 

effective  values  being  used  throughout.  Letting  <£  be  the  max- 
imum value  of  the  field  flux  and  reckoning  time  in  electrical  de- 
grees from  the  instant  when  the  field  flux  is  maximum,  at  any 
time  8,  the  instantaneous  field  flux  is 

<£f=<£cos8  (3) 

and  the  transformer  flux  is 

<£t  =  S<f>  sin  «  (4) 

These  are  the  fundamental  magnetic  equations  of  the  ideal 
repulsion  motor. 

If  at  a  certain  speed  S,  the  effective  value  of  e.m.f.  across  the 
field  coil  be  F,  requiring  an  effective  flux  of  <£f,  then  across  the 
transformer  coil  there  will  be  an  effective  e.m.f.  of 

T=nSF  (5) 

due  to  the  flux  S<f>r  Since  the  fluxes  are  in  time-quadrature, 
the  e.mf.s  are  likewise  in  time  quadrature,  so  that  the  impressed 
e.m.f.  E  must  have  a  value  such  that 

E  =  Vp*  +  T2  (6) 

This  is  the  fundamental  electromotive  force  equation  of  the  re- 
pulsion motor. 

The  current  which  flows  through  the  field  coil  is 

7=T  (7) 

where  X  is  the  inductive  reactance  of  the  field  coil.  Equation 
(7)  gives  the  value  of  the  primary  circuit  current  and  is  the 
fundamental  primary  current  equation. 

The  secondary  armature  current  in  general  consists  of  two 
components,  that  equal  in  magnetomotive  force  and  opposite  in 
phase  to  the  primary  transformer  current,  and  that  necessary 
to  produce  the  flux  in  line  with  the  brushes.  With  a  ratio  of 
effective  armature  turns  to  field  turns  of  a,  the  opposing  trans- 
former current  is 


and  the  current  which  produces  the  transformer  poles  is 

/,=f 


24  The  Sibley  Journal  of  Engineering. 

These   component   currents   are  in  time-  quadrature,  so  that  the 
resultant  secondary  current  is 


This  is  the  fundamental  equation  for  the  secondary  current. 
Combining  (8)  (9)  and  (10) 


It  has  been  seen  that  the  e.m.f.  T  is  in  time- quadrature  to  the 
field  circuit  e.m.f.,  F.  Now  the  current  is  in  time- quadrature 
with  F,  and  hence,  is  in  time-phase  with  T.  Therefore,  of  the 
total  primary  e.m.f.  E,  the  part  T  is  in  phase  with  the  current, 
from  which  fact  it  is  seen  that  the  power  factor  is 

COS0  =  J  (12) 

Power, 

Torque, 

P      IT      ISnF 


D  =  InF  =  InXI  =  PnX  (  14) 

E2  =  F2  +  T2  =  F2  (i+SV)  (15) 


when  n  =  i,  that  is  at  /8  =  45°  see  (i) 

£ 

I  =  —  and  is  constant  at  all  speeds. 
aX 

when  6*  =  i,  that  is  at  synchronism  for  any  value  of  n. 

77 

7a  =  —  -  which  is  seen  to  be  equal  to  the  primary 
aX 

current  at  starting,  (when  a  =  i  ) 

when  S  =  i  the  secondary  current 


Repulsion  Motor. 


and  leads  the  primary  current  by  angle  cotan"1  n  =  ft  or  angle 
of  brush  shift.     See  equation  (i). 


f/C.3.  -  DIAGRAM  Of  IDEAL.   REPULSION    MOTOR 


The  above  equations  can  be  expressed  graphically  by  a  simple 
diagram  as  shown  in  Fig.  3.  The  diagram  is  constructed  as 
follows  :  OE  is  the  constant  line  e.m.f.  OA  at  rt.  angles  to  OE 
is  the  line  current  at  starting,  OB  A  is  a  semicircle,  OF  in  phase 
opposition  to  OA  is  the  secondary  current  at  starting.  ODFis 
a  semicircle.  OG,  in  phase  with  OA,  is  the  secondary  current 
at  infinite  speed.  OHG  is  a  semicircle.  It  will  be  noted  that 
the  ratio  OA  to  OG  is  na  :  i  and  ratio  of  OA  to  OF  is  a  :  n. 

Distances  measured  from  P  in  the  direction  of  T  represent 
speed. 

The  characteristics  of  the  machine  may  be  found  at  once  from 
Fig.  3.  Assuming  any  speed  as  PS,  draw  OS  intersecting  the 
circle  OB  A  at  B.  From  point  G  draw  line  GK  parallel  to  OS. 
Join  O  and  K. 


26  The  Sibley  Journal  of  Engineering. 

OK  is  secondary  current  ; 
OB  is  primary  current  ; 
EOS  is  primary  angle  of  lag  ; 
BC\$  power  component  of  primary  current  ; 
BC  is  power  (to  proper  scale)  ; 
OC  is  torque  (to  proper  scale)  ; 
DOK  is  angle  of  lead  of  secondary  current. 
At  synchronous   speed    (S  =  i),  cotan  6  =  n,  hence  scale  of 
speed  can  readily  be  located. 
OD  =  7t,  see  equation  (7). 
OH=  Iv  see  equation  (8). 
The  proof  of  the  construction  of  diagram  of  Fig.  3  is  as  follows  : 

cos0  =  J  Bq.  (ii) 

E*  =  r2  +  F*  Bq.  (6) 

T=  SnF  Bq.  (5) 


^=l+SV  (20) 

T  Sn 

'£-ST+sw 

Power  component  of  primary  current 

(22) 


Quadrature  component  of  primary  current 


/q  =  AT(i  -f  5V 


cotan  0  =  Sn  (25) 

The  cotangent  of  the  angle  of  lag  is  directly  proportional  to 
the  speed,  the  proportionality  constant  being  the  ratio  of  trans- 
former to  field  turns. 


Repulsion  Motor.  27 


(26) 


Torque  is  proportional  to  quadrature  component  of  the 
primary  (for  given  e.m.f.)  the  proportionality  constant  being  the 
ratio  of  transformer  to  field  turns. 


(27) 


Torque  varies  as  the  square  of  the  primary  current  and  in  this 
respect  is  independent  of  the  speed  or  the  e.m.f. 

A  comparison  of  equations  (26)  and  (27)  reveals  an  interest- 
ing property  of  a  circle.  In  Fig.  3  assuming  the  diameter  A  O 
to  be  unity,  O  C  at  all  valnes  of  angle  6  equals  the  square  of  OB. 

From  equation  (27)  it  is  seen  that  the  torque  is  at  all  times 
positive,  even  when  6*  is  negative.  Hence  machine  acts  as 
generator  at  negative  speed.  For  the  determination  of  the 
generator  characteristics  it  is  necessary  to  construct  the  semi- 
circle omitted  in  each  case  in  Fig.  3. 

It  is  interesting  to  observe  that  the  construction  of  the  diagram 
of  Fig.  3  can  be  completed  at  once  when  points  F,  O,  G  and  A 
and  E  are  located.  Thus  the  complete  performance  of  the  ideal 
repulsion  motor  *;can  be  determined  when  E,  X,  n  and  a  are 
known.  In  the  construction  for  ascertaining  the  value  of  the 
secondary  current,  it  will  be  seen  that  O  K  is  equal  to  the  vector 
sum  of  O  D  and  O  H,  giving  the  vector  O  K.  From  the  proper- 
ties of  vector  co-ordinates  it  will  be  noted  that  the  point  K 
is  located  on  the  semicircle  F  K  G  whose  center  lies  in  the  line 
FOG.  Therefore  if  G  and  F  be  located,  the  inner  circles 
F  D  O  and  O  HG  need  not  be  drawn,  since  the  point  K  can  be 
found  as  the  intersection  of  the  line  drawn  parallel  to  O  B  from 
G  with  the  circular  arc  FK  '  G. 

It  is  to  be  carefully  noted  that  the  above  discussion  refers  to 
ideal  conditions  which  can  never  be  realized.  The  circuits  have 
been  considered  free  from  resistance  and  leakage  reactance  while 
all  iron  losses,  friction,  and  brush  short  circuiting  effects  have 
been  neglected.  The  resistance  and  leakage  reactance  effects 
can  quite  easily  be  taken  into  account,  but  the  remaining  dis- 
turbing influences  are  subject  to  considerable  error  in  approxi- 
mating their  values,  due  primarily  to  the  difficulty  in  assigning 
to  iron  any  constant  in  connection  with  its  magnetic  phenomena. 
It  is  to  be  regretted  that  the  so-called  complete  equations  for  ex- 
pressing the  characteristics  of  this  type  of  machinery  with  al- 


28  The  Sibley  Journal  of  Engineering. 

most  no  exception  neglect  these  disturbing  influences,    and  yet 
these  same  equations  are  given  forth  by  the  various  writers  as 
though  they  represented  the  true  conditions  of  operation. 
In  the  ideal  motor  the  apparent  impedance  is 


+.5V  (28) 

apparent  resistance  is 

R  =  Zcos  0  =  XSn  (29) 

since 


cos  0  =  _  ;    T=  SnF\  and  E  = 
E 

hence 

~  ^  V  =  v/i  +  5V 

apparent  reactance  is 

since 


i  +  5V       Vi  +  5V 

Rt  =  resistance  of  field  coil 
Rt  =  resistance  of  transformer  coil 
R&  =  resistance  of  armature  coil 
X&  =  reactance  of  armature  coil 
Xt  =  reactance  of  transformer  coil 
Xi  =  reactance  of  field  coil 
then  copper  loss  of  motor  circuits  will  be 

72  (Rt  +  R^}  4-  I*R. 


hence 


E  Vn*  +  52 
y'-«A-^/I  +  5V 

/=^7^  (J7) 


/.-^±£  (32) 


and  copper  loss  will  be 


>m 


\(Rt 


Repulsion  Motor.  29 


(33) 


where  Rm  is  the  effective  equivalent  value  of  the  motor  circuit 
resistance,  that  is 


R,  =  R,  +  JRt  +  -*.  (34) 

Similarly  it  may  be  shown  that  the  effective  equivalent  value 
of  the  leakage  reactance  of  the  motor  circuits  is 

.  (35) 


If  these  valves  be  added  to  the  apparent  resistance  and  react- 
ance of  the  ideal  motor  the  corresponding  effects  will  be  repre- 
sented in  the  resultant  equations  thus 


^±^\  £&  (36) 

a      J 


R  =  XSn  +  Xt  +  Xt 

and 

t  (37) 


a 
+  X*  from  (36)  and  (37)  (38) 

E  ,  ^. 

=z  (39) 

Input  =  .£7  cos  0  (40) 

output  =  £Ycos  B  —  PRm  =  P  (41  ) 

p 

torque  =  —  =  D,  etc.  (42) 

*J 

It  will  be  noted  that  the  short  circuiting  by  the  brush  of  a 
coil  in  which  an  active  e.m.f.  is  generated  has  thus  far  not  been 
considered.  Referring  to  Fig.  2,  it  will  be  seen  that  at  any 
speed  5  there  will  be  generated  in  the  coil  under  the  brush  by 
dynamo  speed  action  an  e.m.f. 

E,  =  K^S  (43) 

where  K  is  constant.  This  e.m.f.  is  in  time-phase  with  the 
flux  <£t.  In  this  coil  there  will  also  be  generated  an  e.m.f.  by 
the  transformer  action  of  the  field  flux,  such  that, 

Et  =  A>f  (44) 

This  e.m.f.  is  in  time-  quadrature  to  <£f.  Since  <£f  and  <£t  are  in 
time  quadrature  the  component  e.m.f.s  acting  in  the  coil  under 


30  The  Sibley  Journal  of  Engineering. 

the  brush  are  in  time-phase   (opposition)   so  that  the   resultant 
e.m.f.  is 

-  -S^t)  (45) 

Eq.  (2)  (46) 

Since  for  constant  frequency  of  supply  current,  F  is  propor- 
tional to  <£f  we  may  write  <£f  =  C  F,  C  being  a  constant  depend- 
ing on  the  number  of  field  turns. 

^,=  CE=^  -2=~  Eq.  (16)  (47) 

hence 


which  becomes  zero  at  d=  ^S  =  i ,  that  is  at  synchronism  when 
operated  as  either  a  motor  or  a  generator.  Above  synchronism 
/sb  increases  rapidly  with  increase  of  speed. 

The  friction  loss  can  best  be  taken  into  account  by  considering 
the  friction  torque  as  constant  (=  d)  and  subtracting  this  value 
from  the  delivered  electrical  torque  so  that  the  active  mechanical 
torque  becomes, 

Torque  =  D  —  d  (49) 

While  the  effect  of  the  iron  loss  is  relatively  small  as  concerns 
the  electrical  characteristics  of  the  machine  it  is  obviously  in- 
correct to  neglect  it  when  determining  the  efficiency.  For  pur- 
pose of  analysis  it  is  convenient  to  divide  the  core  material  into 
three  parts,  the  armature  the  field  and  the  transformer  portions. 
Since  the  frequency  of  the  reversal  of  the  flux  in  both  the  trans- 
former and  the  field  portions  is  constant  the  losses  therein  will 
depend  only  upon  the  flux.  Thus  considering  hysteresis  only, 
the  transformer  iron  loss  is 

H,  =  L$l*  (50) 

where  L  is  a  constant  depending  upon  the  mass  of  the  core 
material  similarly  the  field  iron  loss  is 

Ht-Mtf*  (51) 

M  being  a  constant 

H,+  Ht=tf"(M+SL}  Eq.  (2)  (52) 

Since  both  the  field  and  the  transformer  fluxes  pass  through 
the  armature  core  and  these  two  fluxes  are  of  the  same  frequency 
but  displaced  in  quadrature  both  in  mechanical  position  and  in 


Repulsion  Motor.  31 

time-phase  relation,  the  resultant  is  an  elliptical  field  revolving 
always  at  synchronous  speed,  having  one  axis  in  line  with  the 
transformer  and  the  other  in  line  with  the  field,  the  values  being 
v/2  ^t  and  \/2<i>f  respectively:  The  value  of  the  two  axes  may 
be  writen  thus 

x/2  -S^t  and  -v/2  $f 

At  synchronous  speed  of  the  armature  the  two  become  equal  and 
since  no  portion  of  the  iron  is  then  subjected  to  reversal  of  mag- 
netism the  iron  loss  of  the  armature  core  is  of  zero  value.  At 
other  speeds,  while  the  revolving  elliptical  field  yet  travels  syn- 
chronously, the  armature  does  not  travel  at  the  same  speed,  so 
that  certain  sections  of  the  armature  core  are  subjected  to 
fluctuations  of  magnetism  while  others  are  subjected  to  complete 
reversals,  the  sections  continually  being  interchanged.  It  is  due 
to  this  fact  that  no  correct  equation  can  be  formed  to  represent 
the  core  loss  of  the  armature  at  all  speeds,  since  the  behavior  of 
iron  when  subjected  to  fluctuating  magnetism  cannot  be  reduced 
to  a  mathematical  expression. 


ALTERNATING  CURRENT  COMMUTATOR  MOTORS. 
II.  REPULSION-SERIES  MOTOR.* 


A.  s. 

A  type  of  motor  closely  related  to  the  repulsion  machine  in 
the  performance  of  its  magnetic  circuits  is  the  compensated 
series  motor  shown  in  Fig.  4.  Its  electrical  circuits  seem  to  be 
those  of  a  series  machine  with  the  addition  of  a  second  set  of 
brushes,  AA,  placed  in  mechanical  line  with  the  field  coil  and 
short-circuited  upon  themselves.  The  transformer  action  of  this 
closed  circuit  is  such  that  the  real  power  which  the  motor  re- 
ceives is  transmitted  to  the  armature  through  this  set  of  brushes, 
while  the  remaining  set,  BB,  which  in  the  plain  series  motor  re- 
ceives the  full  electrical  power  of  the  machine,  here  serves  to 
supply  only  the  wattless  component  of  the  apparent  power. 


TWO  POLl  MOD£L    Of  IO£AL 
RCPVL&ON-SEWS  MOTOR. 
FIG.-+. 

This  complete  change  in  the  inherent  characteristics  of  the 
series  machine  by  the  mere  addition  of  two  brushes  renders  the 
study  of  this  type  of  motor  especially  interesting. 

For  purpose  of  analysis,  assume  an  ideal  motor  without  resist- 
ance or  local  leakage  reactance  and  consider  first  the  conditions 

*  Abstract  of  thesis  for  Ph.D.  degree,  Cornell  University. 


34 

when  the  armature  is  at  rest.  When  a  certain  e.m.f.,  E,  is  im- 
pressed upon  the  motor  terminals,  the  counter  magnetizing 
effect  of  the  current  in  the  brush  circuits,  AA,  is  such  that  the 
e.m.f.  across  the  transformer  coil  is  of  zero  value,  while  that 
across  the  armature  is  E,  Thus  when  S=o,  letting  Et  =  trans- 
former e.m.f.  and  E&  —  armature  e.m.f., 

£t  =  o,  and£a=E  (53) 

It  is  evident  also  that  when  S  =  O  the  flux  through  the  arma- 
ture in  line  with  the  brushes  A  A  will  be  of  zero  value,  so  that 

4>t  =  0  (54) 

L,et  <j>{  be  the  flux  through  the  armature  in  line  with  the 
brushes  BB.  This  flux,  neglecting  hysteretic  effects,  is  in  time- 
phase  with  the  line  current  and  produces  by  its  rate  of  change 
through  the  armature  turns  a  counter  e.m.f.  of  value  E^=E, 
giving  to  the  armature  circuit  a  reactance  when  stationary,  of  X. 
The  relation  which  exists  between  the  flux,  the  frequency,  and 
the  number  of  armature  turns  can  be  expressed  thus, 

(55) 


V  2    I0 

where 

f=  frequency  in  cycles  per  second 

N  =  effective  number  of  armature  turns 

<£m  =  maximum  value  of  flux. 

If  C  be  the  actual  number  of  conductors  on  the  armature,  the 

£• 

actual  number  of  turns  will  be  —  .     These  turns  are  evenly  dis- 

tributed over  the  surface  of  the  armature,  so  that  any  flux  which 
passes  through  the  armature  core  will  generate  in  each  individual 
turn  an  e.m.f.  proportional  to  the  product  of  the  cosine  of  the 
angle  of  displacement  from  the  position  giving  maximum  e.m.f. 
and  the  value  of  the  maximum  e.m.f.  generated  by  transformer 
action  in  the  position  perpendicular  to  the  flux,  or  the  average 

e.m.f.  per  turn  will  be  2  times  the  maximum.     The  —  turns  are 

7T  2 

connected  in  continuous  series,  the  e.m.f.  in  each  half  adding  in 
parallel  to  that  in  the  other  half,  so  that  the  effective  series  turns 

equal   —  .     Thus,  finally 

N=2^=^  (56) 

7T    4  2  7T 


35 


and  ^,=  (57) 

V  2   I08 

The  value  of  the  reactance  will  depend  inversely  upon  the  re- 
luctance of  the  paths  through  which  the  armature  current  must 
force  the  flux.  The  major  portion  of  the  reluctance  is  found  in 
the  air-gap,  and  with  continuous  core  material  and  uniform  air- 
gap  around  the  core,  the  reluctance  will  be  practically  constant 
xin  all  directions  and  will  be  but  slightly  affected  by  the  change 
in  specific  reluctance  of  the  core  material,  provided  magnetic 
saturation  is  not  reached.  In  the  following  discussion  it  will  be 
assumed  that  the  reluctance  is  constant  in  the  direction  of  both 
sets  of  brushes,  and  that  the  core  material  on  both  the  stator  and 
rotor  is  continuous. 

When  dealing  with  shunt  circuits  it  is  convenient  to  analyze  the 
various  components  of  the  current  at  constant  e.m.f.,  or  assuming 
an  e.m.f.  of  unity,  to  analyze  the  admittance  and  its  components. 
When  series  circuits  are  being  considered,  however,  the  most 
logical  method  is  to  deal  with  the  e.m.f.'s  for  constant  current, 
or  to  assume  unit  value  of  current  and  analyze  the  impedance 
and  its  various  components.  In  accordance  with  the  latter  plan, 
it  will  be  assumed  initially  that  one  ampere  flows  through  the 
main  motor  circuits  at  all  times  and  the  various  e.m.f.'s  (im- 
pedances) will  thus  be  investigated. 

An  inspection  of  Fig.  4  will  show  that  one  ampere  through 
the  armature  circuit  by  way  of  the  brushes  BB  will  produce  a 
definite  value  of  flux  independent  of  any  changes  in  speed  of  the 
rotor,  since  there  is  no  opposing  magneto-motive  force  in  any 
inductively  related  circuit.  From  this  fact  it  follows  that  on 
the  basis  of  unit  line  current  <£a  has  a  constant  effective  value, 
although  varying  from  instant  to  instant  according  to  an 
assumed  sine  law.  As  will  appear  latter,  while  both  the  current 
through  the  armature  and  the  flux  produced  thereby  have  un- 
varying, effective  values  and  phase  positions,  the  apparent 
reactance  of  the  armature  is  not  constant,  but  follows  a  parabolic 
curve  of  value  with  reference  to  change  in  speed. 

When  the  armature  travels  at  any  certain  speed  the  conductors 
cut  the  flux  which  is  in  line  with  the  brushes  BB  and  there  is 
generated  at  the  brushes  A  A  an  electro-motive  force  proportional 
at  each  instant  to  the  flux  <f>f  and  hence  in  time-phase  with  <£f,  or 
with  the  armature  current  through  BB. 


36 


m  =  maximum  value  of  <£f  ,  then  the  maximum  value  of 
the  e.m.f.  generated  at  A  A  due  to  dynamo  speed  action  will  be, 

*.-%? 

where    V  is  revolutions  per  second.     The  virtual  value  of  this 
electro-motive  force  will  be 

-  (59) 


A  comparison  of  (59)  and  (57)  will  show  that  at  a  speed  V 
revolutions  per  second  such  that  V—f  in  cycles  per  second, 
^v  =  ^ffor  any  value  of  <£m.  Consequently,  the  speed  e.m.f. 
due  to  any  flux  threading  the  armature  turns,  at  synchronism 
becomes  equal  to  the  transformer  e.m.f.  due  to  the  same  flux 
through  the  same  turns.  Et  is  in  time-  quadrature  and  E^  in 
time-phase  with  the  flux  at  any  speed,  hence,  Ey  is  in  time- 
quadrature  with  £t  or  in  time-phase  with  the  line  current. 

The  brushes  AA  remain  at  all  times  connected  directly  to- 
gether by  conductor  of  negligible  resistance  so  that  the  resultant 
e.m.f.  between  the  brushes  must  remain  of  zero  value.  On  this 
account  when  an  e.m.f.  Ev  is  generated  between  the  brushes  by 
dynamo  speed  action,  a  current  flows  through  the  local  circuit 
giving  a  magneto-motive  force  such  that  the  flux  produced 
thereby  generates  in  the  armature  conductors  by  its  rate  of 
change,  an  e.m.f.  equal  and  opposite  to  Ey.  This  flux,  <£t,  is 
proportional  to  Ey  and  being  in  time-  quadrature  thereto,  is  in 
time-phase  with  E^  or  in  time-quadrature  with  <£r 

From  the  transformer  relations  it  is  seen  that 

£    '      •        ow 

V  2   I08 

where  </2  $t  ig  maximum  value  of  flux  due  to  current  through 
brushes  A  A  .     See  (57). 

£V=G^  (61) 

where  G  is  a  proportionality  constant. 

L,et  6*  be  the  speed,  with  synchronism  as  unity,  then 

EV  =  SE<  (62) 

and 

*t=S*r,  (63) 

effective  values  being  used.     This  is  the  fundamental  magnetic 
equation  of  the  repulsion-series  motor. 


37 

Flux  <£t  passes  through  the  transformer  turns  on  the  stator  in 
line  with  the  brushes  AA  as  shown  in  Fig.  4  and  generates 
therein  by  its  rate  of  change  an  e.m.f.  £r  such  that 

E,  =  n  Ev  (64) 

where  n  is  the  ratio  of  effective  transformer  to  armature  turns. 
This  e.m.f.  is  in  phase  with  Ev,  in  quadrature  with  Et  and  hence 
is  in  phase  opposition  with  the  line  current  and  produces  the 
effect  of  apparent  resistance  in  the  main  motor  circuits. 
Combining  (62)  and  (64) 

E,=  SnE,  (65) 

Since  Et  is  the  transformer  e.m.f.  in  the  armature  circuits  due 
to  constant  effective  value  of  flux  from  one  ampere,  we  may 
write 

Et~X  (66) 

where  X  is  the  stationary  reactance  of  the  armature  circuit,  so 
that  the  apparent  resistance  of  the  transformer  circuit  is 

R  =  SnX  (67) 

Under  speed  conditions  the  armature  conductors  cut  the  flux 
in  line  with  the  brushes  A  A,  and  there  is  generated  thereby  an 
e.m.f.  which  appears  as  a  maximum  at  the  brushes  BB.  This 
e.m.f.  is  in  phase  with  <£t,  in  quadrature  with  <£f  and  in  phase 
opposition  to  Er  If  Es  be  the  value  of  this  e.m.f.  we  may  write, 

E,  =  <V*.  *SJ?  (68) 

N/2    I08 

from  dynamo  speed  relations.      Comparing  (60)  and  (68)  and 
remembering  that  /is  unity  in  terms  of  speed,  there  is  obtained 

£*  =  $£,  (69) 

from  (62)  and  (66) 

£s  =  S*£t.=  S2X  (70) 

Therefore  the  e.m.f.  across  the  armature  at  B  B  will  be 

Em*.£t-£.  =  X(i-S')  (71) 

This  e.m.f.  is  in  quadrature  with  the  line  current  and  is  in 
effect  an  apparent  reactance,  so  that  the  apparent  reactance  of 
the  motor  circuits  which  is  confined  to  the  armature  winding  is 

X=X(i-S*)  (72) 

The  apparent  impedance  of  the  motor  circuits  at  speed  6*  is 

X*  +  X*i-S**     (73) 


38 

This  is  the  fundamental  impedance  equation  of  the  ideal  repul- 
sion-series motor. 
The  power  factor  is 

cos  6  =  *  = SnX 

7  -   /  /"   t~*   -- 1S-\  2 i         V2    /  _  O2\2  \/T-/ 

The  line  current  is 


(75) 


The  power  is, 

/72     Q*    V"-M 

(76) 


It  will  be  noted  that  both  the  power  and  the  power  factor  re- 
verse when  S  is  negative.  Thus  the  machine  becomes  a  gener- 
ator when  driven  against  its  torque. 

The  wattless  factor  is, 

Sin.  =  4=-        _*('">)  (77) 

Z  ' 


and  becomes  negative  when  6*  is  greater  than  i,  so  that  above 
synchronism  when  operated  as  either  a  generator  or  motor  the 
machine  draws  leading  wattless  current  from  the  supply  system. 
At  ,S  =  i,  Sin  0=o,  which  means  that  the  power  factor  is  unity 
at  synchronous  speed,  as  may  be  seen  also  from  eq.  (74). 
At  S  =  o, 

'  * 

At  5  =  i,  /=  -—  That  is,  at 

n  X 

synchronism  the  line  current  is  equal  to  the  current  at  start  di- 
vided by  the  ratio  of  transformer  to  armature  turns.  If  N  =  i, 
the  current  at  synchronism  is  of  the  same  value  as  at  start  but 
the  power  factor  which  at  start  was  o  has  a  value  of  i  at  syn- 
chronism. This  interesting  feature  will  be  touched  upon  later. 
The  torque  is 

*  nX         (78) 


*  S*  ri>  +  X2  (  i  -  S2)"2 

and  is  maximum  at  maximum  current  and  retains  its  sign  when 
6*  is  reversed. 

When  S  =  o  the  secondary  current,  /8,  is  nl,   and  is  in  phase 


39 


opposition  with  the  transformer  current  /.     See  Fig.  4     When 


/  = 


+ 


and  at  any  speed  S, 
P  =  !  ^/n*  +  S2  (79) 


2  -f- 


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CHARACTERISTICS     Of    IDEAL      REPULSION  -  SERIES     MOTOR. 
FIG-  cf. 

Ill  Fig.  5  are  shown  the  results  of  calculations  for  a  certain 
ideal  repulsion-series  motor  of  which  X=  i  and  n  =  2.  It  is 
seen  that  with  speed  as  abscissa,  the  curve  representing  the  ap- 
parent resistance  of  the  motor  circuits  is  a  right  line  while  that 
for  the  apparent  reactance  is  a  parabola.  At  any  chosen  speed 
the  quadrature  sum  of  these  two  components  gives  the  apparent 
impedance  of  the  motor.  Since  the  scale  for  representing  the 
speed  is  in  all  respects  independent  of  that  used  for  the  apparent 
resistance,  it  is  possible  always  so  to  select  values  for  the  one 
scale  that  a  given  distance  from  the  origin  may  simultaneously 
represent  both  the  resistance  and  the  speed.  This  method  of 
plotting  the  values  leads  to  a  very  simple  vector  diagram  for  rep- 
resenting both  the  value  and  phase  position  of  the  apparent  im- 
pedance at  any  speed,  and  for  determining  the  power- factor  from 
inspection.  Thus  at  any  speed  such  as  is  shown  at  G  the  dis- 


40 

tance  OG  is  the  apparent  resistance,  the  distance  GP  is  the  ap- 
parent reactance,  OP  is  the  apparent  impedance  while  the  angle 
POG  is  the  angle  of  lead  of  the  primary  current  and  its  cosine  is 
the  power- factor. 


SP£CD  IN  P£fJC£/VT. 


CHARACTERISTICS     OF    IDEAL     A£PVLS/<W-S£W£S     MOTOR. 

f/G.-e. 

Fig.  6  gives  the  complete  performance  charactersitics  of  the 
above  ideal  repulsion-series  motor  at  various  positive  and  nega- 
tive speeds  when  operated  at  an  impressed  e.m.f.  of  100  volts. 

It  will  be  noted  that  the  armature  e.m.f.,  which  has  a  certain 
value  at  standstill,  decreases  with  increase  of  speed,  becomes  zero 
at  synchronism  and  then  increases  at  higher  speeds.  The  trans- 
former e.m.f.  is  zero  at  starting,  increases  to  a  maximum  at  syn- 
chronism and  then  continually  decreases  with  increase  of  speed. 

The  inductive  portion  of  the  impedance  is  contained  wholly  by 
the  armature  circuit,  while  the  non-inductive  is  confined  to  the 
transformer  coil;  thus  the  power-factor  is  zero  at  standstill, 
reaches  unity  at  synchronism  and  then  decreases  due  to  the  lag- 
ging component  of  the  motor  impedance  (leading  wattless  cur- 
rent). In  comparison  with  the  ordinary  compensated  series 
motor  whose  armature  e.m.f.  is,  for  the  most  part,  non-inductive 
and  continually  increases  with  increase  of  speed,  and  whose  in- 
ductive field  e.m.f,  decreases  continually  with  increase  of  speed 
and  whose  power-factor  never  reaches  unity,  the  repulsion-series 
motor  furnishes  a  most  striking  contrast.  The  machine  resem- 


bles  the  repulsion  motor  in  regard  to  its  magnetic  behavior,  but 
the  performance  of  its  electric  circuits  differs  from  that  of  the 
repulsion  motor  due  to  the  fact  that  the  speed  e.m.f.  introduced 
into  the  armature  circuit  BB  (Fig.  4)  which  has  been  substituted 
for  the  field  coil  of  the  repulsion  motor  (See  Fig.  2)  is  in  a  di- 
rection continually  to  decrease  the  apparent  reactance  of  the 
field  circuit  and  thus  to  decrease  the  inductive  component  of  the 
impedance  of  the  circuits  and  to  improve  the  power  factor  and 
the  operating  characteristics.  It  is  an  interesting  fact  that 
under  all  conditions  of  operation  the  e.m.f.  in  the  coils  short  cir- 
cuited by  the  brushes  BB  is  of  zero  value,  so  that  no  objectional 
features  are  introduced  by  substituting  the  armature  circuit  for 
the  field  coil  of  the  repulsion  motor,  while  the  performance  is 
materially  improved.  Experiments  show  that  even  with  currents 
of  many  times  normal  value  and  at  the  highest  commercial  fre- 
quency no  indication  of  sparking  is  found  at  the  brushes  BB. 
This  feature  will  be  treated  in  detail  later. 

An  inspection  of  Fig.  5  and  of  equation  (73)  will  reveal  the 
fact  that  at  synchronism  the  apparent  impedance  is  n  times  its 
value  at  stand  still.  If  n  be  made  unity,  the  apparent  impedance 
at  synchronism  will  be  equal  to  that  at  stand  still,  while  between 
these  speeds  it  varies  inappreciably.  This  means  that  from  zero 
speed  to  .synchronism  the  primary  current  varies  but  slightly, 
and  that  the  torque,  which  is  proportional  to  the  square  of  the 
primary  current  is  practically  constant  throughout  this  range  of 
speed.  These  facts  show  that  a  unity  ratio  repulsion  series- 
motor  is  a  constant  torque  machine  at  speeds  from  negative  to 
positive  synchronism,  the  relative  phase  position  of  the  current 
and  the  e.m.f.  changing  so  as  always  to  cause  them  to  give  by 
their  vector  product  the  power  represented  by  the  torque  at  the 
various  speeds.  Above  synchronism  the  torque  decreases  con- 
tinually, tending  to  disappear  at  infinite  speed. 

Any  desired  torque-speed  characteristic  within  limits  can  be 
obtained  by  giving  to  n  a  corresponding  value,  the  torque  at 
synchronism  being  equal  to  the  starting  torque  divided  by  the 
square  of  the  ratio  of  transformer  to  armature  turns. 

In  connection  with  the  discussion  of  the  expression  for  deter- 
mining the  value  of  the  torque  it  is  well  to  mention  the  fact  that 
the  commonly  accepted  explanations  as  to  the  physical  phenom- 
ena involved  in  the  production  of  torque  must  be  somewhat 
modified  if  actual  conditions  of  operation  known  to  exist  are  to 


be  represented.  Referring  to  Fig.  4,  it  will  be  noted  that  when 
the  armature  is  stationary  there  exists  no  magnetism  in  line  with 
the  brushes  A  A,  so  that  the  current  which  enters  the  armature 
by  way  of  the  brushes  BB  could  not  be  said  to  produce  torque 
by  its  product  with  magnetism  in  mechanical  quadrature  with  it. 
Similarly,  the  flux  in  line  with  the  brushes  BB  could  not  be  said 
to  be  attracted  or  repelled  by  magnetism  which  does  not  exist. 
That  the  current  through  AA  produces  torque  by  its  product 
with  the  magnetism  due  to  current  through  BB  would  be  con- 
trary to  accepted  methods  of  reasoning,  since  both  currents  flow 
in  the  same  structure,  yet,  as  concerns  the  torque,  the  effect  is 
quite  the  same  as  though  the  flux  in  line  with  the  brushes  BB 
were  due  to  current  in  a  coil  located  on  the  field  core.  (As 
shown  in  Fig.  2  for  the  ordinary  repulsion  motor.) 

The  calculated  impedance  characteristics  shown  in  Fig.  5  are 
based  on  arbitrarily  assumed  constants  of  a  repulsion-series 
motor  under  ideal  conditions.  It  is  obviously  impossible  to  ob- 
tain such  characteristics  from  an  actual  motor,  since  all  losses 


-/«_ 


'SPEED    IN  IQO  R.P.M. 

Q    +2,    +4- 


+8 


-1-4 


T<Y 


*H 


-z 


-3 


TE&T  OF  REPULSION  SERIES  MOTOR-ACTIVE  FACTORS  OF  OPERATION 

nc  7. 

and  minor  disturbing  influences  have  been  neglected  in  deter- 
mining the  various  values.  As  a  check  upon  the  theory  given 
above,  the  curves  of  Figs.  7  and  8,  as  obtained  from  tests  of  a 
repulsion-series  motor,  are  presented  herewith.  It  will  be  ob- 


43 


served  that  the  apparent  resistance  of  the  transformer  coil  varies 
directly  with  the  speed  and  becomes  negative  at  negative  speed, 
while  the  apparent  reactance  of  the  armature  decreases  with  in- 
crease of  speed  in  either  direction  and,  following  approximately 
a  parabolic  law,  reverses  and  becomes  negative  at  speeds  slightly 
in  excess  of  synchronism.  A  comparison  of  the  general  shape 
of  the  curves  of  Fig.  7  and  Fig.  5  will  show  to  what  extent  the 
assumed  ideal  conditions  can  be  realized  in  practice,  and  it  would 
indicate  that,  as  concerns  the  active  factors  of  operation,  the 
equations  given  represent  the  facts  involved.  The  neglect  of 
the  local  resistance  of  the  transformer  circuit  leads  to  the  dis- 
crepancy between  the  theoretical  and  observed  curves  as  found 
at  zero  speed,  the  latter  curve  indicating  a  certain  apparent  re- 
sistance when  the  armature  is  stationary.  Similarly  at  synchro- 
nous speed  the  observed  apparent  reactance  of  the  armature  is 
not  of  zero  value  due  to  the  local  leakage  reactance  of  the  circuit. 
In  the  determination  of  the  theoretical  curves  only  active 
factors  have  been  considered,  and  it  has  been  shown  that  the 
apparent  reactance  of  the  motor  circuits  is  confined  to  the  arma- 
ture, while  the  e.m.f.  counter  generated  in  the  transformer  coil 
gives  the  effect  of  apparent  resistance  located  exclusively  within 
this  coil.  The  neglected  disturbing  factors,  the  apparent  resist- 
ance of  the  armature  and  the  apparent  reactance  of  the  trans- 
former, are  of  relatively  small  and  practically  constant  value 
SPEED  IN  100 


8 

:       f- 

<a 

V 

.*> 

1 

/J 

c 

0 

1 

1 

/ 

/ 

-f-     3 

V 

^ 

1 

I 

^/ 

/ 

+  2- 

^e 

^ 

°,/ 

P 

^ 

&  6 

3^ 

°n^ 

/Urn 

i  oft 

f^ 

\ 

<r- 

"of( 

ec 

c 

fo 

TC  e 

°f 

Tr 

a  n  i 

fo, 

»T7« 

T* 

*->> 

^ 

& 

4  T| 

s 

$ 

•2 

\i 

^ 

*i 

I 

TEST  Of  REPULSION  iS£R/E$  MOTOR-DISTURBING  FACTORS  OF  OPERATION. 

FIG.  Q. 


44 

throughout  the  operating  range  of  speed  from  negative  to  posi- 
tive synchronism,  but  they  become  of  prime  importance  when 
the  speed  exceeds  this  value  in  either  direction,  as  shown  by  the 
curves  of  Fig.  8  obtained  from  the  test  of  a  repulsion-series 
motor  giving  the  curves  of  Fig.  7.  The  predominating  influence 
of  the  disturbing  factors  above  synchronism  is  attributable 
largely  to  the  effect  of  the  short  circuit  by  the  brushes  A  A 
(Fig.  4)  of  coils  in  which  there  is  produced  an  active  e.m.f.  by 
combined  transformer  and  speed  action.  This  short  circuiting 
effect  will  be  treated  in  detail  later. 

The  resistance  and  local  leakage  reactance  of  the  coils  may  be 
included  in  the  theoretical  equations  as  follows : 
Ivet   Rt  =  resistance  of  transformer  coil 

R&  =  resistance  of  armature  circuit 

Ra  =  resistance  of  secondary  circuit 

Xt  =  leakage  reactance  of  transformer 

XA  =  leakage  reactance  of  armature 

Xn  —  leakage  reactance  of  secondary  circuit 
then  copper  loss  of  motor  circuits  will  be 

7'(*t +  *.)+/.'*,,  (81) 

/.-^^/STf-J"1  (82) 

/'    IX    +    ^a    +    <X    +    ^2)   *J     =    /2  *m  (83) 

where  Rm  is  the  effective  equivalent  value  of  the  motor  circuit 
resistance,  that  is, 

*m   =   ^t   +    R*    +    O2    +    ^2)   ^s  (84) 

Similarly  it  may  be  shown  that  the  effective  equivalent  value 
of  the  leakage  reactance  of  the  motor  circuits  is 

Xm  =  Xt  +  X^  +  («•  +  S')  X.  (85) 

combining  equations  (84)  and  (85)  with  (73)  the  expression  for 
the  apparent  impedance  of  the  motor  circuits  becomes 


Z=  V(R  +  RmY  +  (X  +  XJ*  =  (86) 


-  51)  +  Xt  +  X&  -f  (**  +  52)  Xay 
.  __  _E  _ 

=  ~*  22 


___  Sn_X_+Jt_ 
= 


45 


Input  =  E  /cos  0  (89) 

Output  =  E  /cos  0  -  P  £m  =  P  (90) 

E*(Sn 
(SnX+Rmy  + 

E1  R 


(SnX+  ^m)2  +  [*  (i  -  S)  -f  A;,]2 

/72     C  7;     "V" 

./^     — —        -  ;:     J-  kJ    //    -^L 


torque  =  D  =      =  TnX  (93) 

o 

The  above  equations,  though  incomplete  on  account  of  neglect- 
ing the  brush  shortening  effect  and  the  magnetic  losses  in  the 
cores,  represent  quite  closely  the  electrical  characteristics  of  the 
repulsion-series  motor  when  operated  between  negative  and  posi- 
tive synchronism,  throughout  which  range  of  speed  the  disturb- 
ing factors  are  of  secondary  importance. 

The  e.m.f.  in  the  coils  short  circuited  by  the  brushes  can  be 
treated  by  a  method  similar  to  that  used  with  the  repulsion 
motor.  Referring  to  Fig.  4,  the  coil  under  the  brush  A  is  sub- 
jected to  the  transformer  effect  of  the  flux,  <j>t,  in  line  with  the 
brushes,  BB,  and  the  dynamo  speed  effect  of  the  flux,  <£t,  in  line 
with  the  brushes  AA. 

Effective  values  being  used  throughout,  the  transformer  e.m.f. 
will  be,  assuming  C  actual  conductors  on  the  armature, 


4 

in  volts  for  one  coil.     See  equation  (57).     This  e.m.f.  is  in  time- 
quadrature  with  </>,.. 

The  dynamo  speed  e.m.f.  in  volts  for  one  coil  will  be, 

CTT   y,~. 

(95) 


4 

See  equation  (59).     This  e.m.f.  is  in  time-phase  with  <£t  and 

hence  is  time-quadrature  with  <£r  Thus  the  electro-  motive  force 
in  the  coil  under  the  brush  A  is 

(96) 


46 

But  F  =  /5and  <£t  =  5>f  (97) 

See  equation  (63),  hence 

F4>t  =  sy*p  (98) 

so  that 

^=^'(i-52)      v!     (99) 

This  resultant   electromotive   force  has  a  value  at  standstill, 
when  6*  is  zero,  of 


'          IirX 

=    -         -  (100) 

C  2  C 


.4 
See  equation  (66)         Thus 

finally,  E^  =  /7r-^  (  i  -  5")  (  101  ) 

2   C 

When  the  armature  is  stationary  the  electro-  motive  force  in  the 
coil  short  circuited  by  the  brush  A  has  the  value  given  by  equa- 
tion (100),  which,  with  any  practical  motor,  is  of  sufficient  value 
to  cause  considerable  heating  if  the  armature  remains  at  rest,  or 
to  produce  a  fair  amount  of  sparking  as  the  armature  starts  in 
motion.  At  synchronous  speed,  however,  this  electro-  motive 
force  disappears  entirely,  and  the  performance  of  the  machine  as 
to  commutation  is  perfect.  As  the  speed  exceeds  this  critical 
value  in  either  the  positive  or  negative  direction,  the  electro- 
motive force  in  the  short-circuited  coil  increases  rapidly,  resulting 
in  a  return  in  an  augmented  form  of  the  sparking  found  at  lower 
speeds  and  producing  the  disturbing  factors  shown  by  the  curves 
of  Fig.  8. 

Since  the  e.m.f.  in  the  coil  under  the  brush  A  reduces  to  zero 
at  both  positive  and  negative  synchronism  and  reverses  with 
reference  to  the  time-phase  position  of  the  line  current  at  speeds 
exceeding  synchronism  in  either  direction,  it  possesses  at  high 
speeds  the  same  time-phase  position  when  the  machine  is  operated 
as  a  generator  as  when  it  is  used  as  a  motor.  The  time-phase  of 
its  reactive  effect  upon  the  current  which  flows  in  the  armature 
through  the  brushes  BB  is  of  the  same  sign  at  high  positive  and 
negative  speeds,  but  reversed  from  the  phase  position  of  the 
effect  at  speeds  below  synchronism.  A  study  of  the  test  curves 
of  Fig.  8  will  show  the  magnitude  of  these  effects,  and  the 


47 

reversal  of  their  time-phase  positions  in  accordance  with  the 
theoretical  considerations. 

With  reversal  of  direction  of  rotation,  the  time-phase  position 
of  the  flux  threading  the  transformer  coil  (Fig.  4)  reverses  with 
reference  to  the  line  current,  and  hence  in  its  reactive  effect 
upon  the  transformer  flux  the  current  in  the  coil  short  circuited 
by  the  brush  A  becomes  negative  at  speeds  above  negative  syn- 
chronism, though  positive  above  synchronism  in  the  positive 
direction.  At  speeds  below  synchronism,  when  the  flux  is  large 
the  e.m.f.  is  small,  and  vice  versa,  so  that  the  reactive  effect  is  in 
any  case  relatively  small  and  of  more  or  less  constant  value.  See 
Fig.  8. 

It  will  be  noted  that  in  analyzing  the  disturbing  factors  no  ac- 
count has  been  taken  of  the  short-circuiting  effect  at  the  brushes 
BB,  Fig.  4.  This  treatment  is  in  accord  with  the  statement 
previously  made  that  the  component  e.m.f.s  generated  in  the 
coils  under  these  brushes  are  at  all  times  of  values  such  as  to 
render  the  resultant  zero.  The  proof  of  this  fact  is  as  follows: 

The  transformer  e.m.f.  in  the  coil  under  B  due  to  flux,  </>t,  in 
line  with  brushes  A  A  is 

•<-lf&     -  (I02) 

See  equation  (94).     This  e.m.f.  is  in  time-  quadrature  with  <£t. 
The  dynamo  speed  e.m.f.  is 


This  e.m.f.  is  in  time-phase  with  <£,.,  in  time  quadrature  with 
t,  and  is  in  phase  opposition  to  er     Thus  the  resultant  e.m.f.  is 

E*  =  *,  ~  e,  -  -  ~  C/>,  -V+d  (  104) 

Since  V  =f  S  and  <£t  =  S  <f>t  from  equations  (97)  and  (63), 


and 

^b  =  °  (106) 

This  theoretical  deduction  is  substantially  corroborated  by  ex- 
perimental evidence,  as  has  been  noted  above.  Even  upon  super- 
ficial examination  such  a  result  is  to  be  expected,  since  the 
vector  sum  of  all  e.m.f.s  in  the  armature  in  mechanical  line  with 
the  short-circuited  brushes  A  A  must  be  zero,  while  the  e.m.f. 
in  the  coil  at  brush  B  must  equal  its  proper  share  of  this  e.m.f.  or 


48 


r  O'TT 

Jg;  *•_«.<>  (107) 

A  similar  course  of  reasoning  allows  of  the  determination  of 
the  electro-motive  force  under  the  brush  A.     See  equation  (71). 


\~*  2  2  *  (^ 

for  unit  current.     For  /  amperes  this  becomes. 

£.=  ££(i-S')  (109) 

See  equation  (101). 

From  the  facts  just  indicated  it  would  seem  that  perfect  com- 
mutation dictates  that  the  electro-motive  force  across  a  diameter 
ninety  electrical  degrees  from  the  brushes  upon  the  armature  be 
at  all  times  of  zero  value.  Methods  for  approximating  this 
condition  will  be  discussed  in  a  later  paper. 

It  has  been  stated  that  the  magnetic  circuits  of  the  repulsion- 
series  motor  are  quite  the  same  as  those  of  the  repulsion  motor. 
The  fluxes  in  line  with  the  two  brush  circuits  under  all  condi- 
tions are  ir  time-quadrature  and  have  relative  values  varying 
with  the  speed  such  that  at  all  times 

4>t  =  S4>t  (no) 

There  exists,  therefore,  at  all  speeds  a  revolving  magnetic  field 
elliptical  in  form  as  to  space  representation.  At  standstill  the 
ellipse  becomes  a  straight  line  in  the  direction  of  the  brushes  BB 
(Fisjp4),  at  infinite  speed  in  either  direction  the  ellipse  would 
again  be  a  straight  line  in  the  direction  of  the  brushes  AA,  while 
at  either  positive  or  negative  synchronism  the  ellipse  is  a  true 
circle,  the  instantaneous  maximum  value  of  the  revolving  mag- 
netism traveling  in  the  direction  of  motion  of  the  armature.  At 
synchronous  speed,  therefore,  the  magnetic  losses  in  the  arma- 
ture core  disappear,  while  the  losses  in  the  stator  core  are  evenly 
distributed  around  its  circumference. 


ALTERNATING  CURRENT  COMMUTATOR  MOTORS. 
III.    COMPENSATED  SERIES  MOTORS.* 

A.  s.  M'AUJSTKR. 

The  combined  transformer  and  motor  features  of  commutator 
type  of  alternating  current  machinery  are  well  exemplified  in  the 
plain  series  motor  as  illustrated  in  Fig.  9.  When  the  rotor  is 


SPEED       E.MF 


or  Ccm*cwr 


FIG.  9.     Plain  Series  Motor. 

stationary,  the  field  and  armature  circuits  of  the  motor  form  two 
impedances  in  series.     Assuming  initially  an  ideal  motor  without 

*  Abstract  of  thesis  for  Ph.D.  degree,  Cornell  University. 


50  Compensated  Series  Motor. 

resistance  and  local  leakage  reactance,  each  impedance  consists  of 
pure  reactance,  the  current  in  the  circuit  having  a  value  such 
that  its  magneto-motive  force  when  flowing  through  the  armature 
and  field  turns  causes  to  flow  through  the  reluctance  of  the  mag- 
netic path  that  value  of  flux  the  rate  of  change  of  which  generates 
in  the  windings  an  electro-motive  force  equal  to  the  impressed. 

If  E  be  the  impressed  e.m.f.,  Ef  the  counter  transformer  e.m.f. 
across  the  field  coil  and  E^  the  counter  transformer  e.m.f.  across 
the  armature  coil,  when  the  armature  is  stationary 

£  =  £,+  £,  (in) 

From  fundamental  transformer  relations  there  is  obtained  the 
equation 

EI  =  2  ,-^    s  >  see  e<i-  (55)  (112) 

V  2   IO 

where    f  =•  frequency  in  cycles  per  second 
Nt  =  effective  number  of  field  turns 
<f>f  =  maximum  value  of  field  flux. 
Similarly 

*-H^ 

where  N&  =  effective  number  of  armature  turns 
<£a  =  maximum  value  of  armature  flux. 

Since  the  field  and  armature  circuits  are  electrically  series  con- 
nected and  are  mechanically  so  placed  as  not  to  be  inductively 
related,  with  uniform  reluctance  around  the  air  gap  the  fluxes  in 
mechanical  line  with  the  two  circuits  being  due  to  the  magneto- 
motive force  of  the  same  current  will  be  proportional  to  the 
effective  number  of  turns  on  the  two  circuits. 

Therefore 


If  n  be  the  ratio  of  effective  field  to  armature  turns 

Nt=nN^  (115) 

and 

<f>f=n<t>&  (116) 

L,et  Cbe  the  actual  number  of  conductors  on  the  armature,  then 

^a  =  —  (seeeq.  56)  (117) 

2  7T 

Under  speed  conditions  the  armature  conductors  cut  the  field 
magnetism   and   there   is  generated  by  dynamo  action  a  counter 


Sibley  Journal  of  Engineering. 


e.m.f.  proportional  to  the  product  of  the  field  flux  and  the  speed, 
in  time-phase  with  the  flux,  in  leading  time  quadrature  with  the 
field  e.m.f.,  Z?f  and  the  armature  e.m.f.  EA  and  in  phase  opposi- 
tion with  the  current. 
Thus 

^  =  ^J  (see  eq-  59)  <II8> 

V  2  IO 

where  Fis  revolutions  per  second  of  bipolar  model. 
Combining  (117)  and  (118) 


If  ,5*  be  the  speed  with  synchronism  as  unity,  then 

V=Sf  (120) 

and 


combining  (113)  (116)  and  (121) 


combining  (112)  (115)  and  (121) 

*•-*&-¥ 

comparing  (122)  and  (123) 

E,-*<E. 

Under  speed  conditions  the  impressed  e.m.f.  is  balanced  by 
three  components,  Ev  in  time  phase  opposition  with  the  line  cur- 
rent and  Et  and  E^  both  in  leading  time  quadrature  with  the 
line  current. 

Thus 

+    E   f  E  (125) 


This  is  the  fundamental  electro-motive  force  equation  of  the  plain 
series  motor  having  uniform  reluctance  around  the  air-gap. 

On  the  basis  of  unit  line  current  the  electro-motive  forces  may 
be  treated  as  impedances,  as  was  done  with  the  repulsion-series 
motor,  so  that  the  impedance  equation  becomes 

^^a^S^-f  (i  +rc2)2  (127) 

where  SnX&  =  R  and  (i  +  n2)  X^  =  X 


52  Compensated  Series  Motor. 

The  power  factor  is 

=  0080=  Sn  (128) 


which  reverses  when  5*   becomes   negative    and   continually   ap- 
proaches unity  with  increase  of  5"  in  either  direction. 
When  5"  =  i  ,  or  at  synchronism 

cos6»  =  -  n  (129) 

Vn*  +  (i  +  n*y 

which  when  n  =  i  or  for  unity  ratio  of  field  to  armature  turns 
becomes 


(I30) 


and  decreases  with  either  an  increase  or   decrease  of  n.      It   is 
apparent  therefore  that  the  power  factor  of  such  a  machine  is  in- 
herently very  low  and  cannot  be  improved  by  a  mere  change  in 
the  ratio  of  field  to  armature  turns. 
The  line  current  is 


/=  ^=    E  _  , 

=  ~Z  22 


The  power  is 


which  becomes  negative  when  5*  reverses,  or  the  machine  operates 
as  a  generator  when  driven  against  its  natural  tendency  to  rota- 
tion. 

The  torque  is 


which   is   maximum   at   maximum   current   and  retains  its  sign 
when  5*  is  reversed. 

At  starting  the  torque  is 

^-|-(iTW  (I34) 

At  synchronous  speed,  the  torque  is 


and 

•A-     (I+**1)1  (I36) 

D          «»+!+«•» 


The  Sibley  Journal  of  Engineering.  53 

which  when  n  is  negligibly  small  approaches  a  value  of  unity  and 
when  n  is  infinitely  large  also  tends  to  reach  a  value  of  unity. 
When  n  =  i  equation  (136)  reduces  to 


-    8 


ths  interpretation  of  which  is  that  the  torque  of  the  unity-ratio 
single-phase,  plain  series  motor  with  uniform  reluctance  around 
the  air-gap  varies  only  20  per  cent,  from  standstill  to  synchro- 
nism, and  therefore,  that  such  a  machine  is  unsuited  for  traction. 
This  statement  applies  to  the  ideal  single-phase  motor  without 
internal  losses  and  must  be  somewhat  modified  to  include  true 
operating  conditions.  The  method  of  treating  the  various  losses 
has  previously  been  discussed  and  will  further  be  enlarged  upon 
in  connection  with  the  compensated  types  of  series  machines.  A 
little  consideration  will  show  that  such  modifications  as  must  be 
introduced  have  a  detrimental  effect  upon  the  characteristics  of 
the  machine,  and  tend  to  lay  greater  stress  upon  the  statement 
just  made.  These  facts  are  graphically  represented  in  the  per- 
formance (impedance)  diagram  of  Fig.  9.  OA  is  the  power  and 
AB  the  reactive  component  of  the  apparent  field  impedance  at 
starting  while  BC  and  CD  are  the  corresponding  power  and  re- 
active components  of  the  apparent  armature  impedance.  The 
power  component  of  apparent  armature  impedance  due  to  dynamo 
speed  action  is  shown  as  DE  or  DF  giving  the  resultant  imped- 
ance under  speed  conditions  of  OE  or  O^and  indicating  an  angle 
of  lag  of  the  circuit  current  behind  the  impressed  e.m.f.  of  EOA 
or  FOA.  The  variation  in  torque  due  to  increase  of  speed  from 
synchronism  to  double  synchronism  with  a  unity  ratio  constant 
reluctance  machine,  as  represented  in  Fig.  9,  would  be  as  the 
square  of  the  ratio  of  OF  to  OE. 

An  inspection  of  equation  (136)  will  reveal  the  fact  that  a 
a  change  in  the  value  of  n  does  not  improve  the  torque  charac- 
teristics of  the  machine  unless  such  change  be  accompanied  with 
an  increase  in  reluctance  of  the  magnetic  structure  in  line  with 
the  brushes  Bv  B2  (Fig.  9).  That  is  to  say,  if  the  mechanical 
construction  is  such  that  equation  (114)  may  be  written 

-"  (I38) 


.        . 

where  m  is  a  constant  of  a  value  many  times  unity,  the  oper- 
ating characteristics  of  the  machine  become  much  improved. 
Thus  equation  (116)  becomes 


54  Compensated  Series  Motor. 

o, ===  mn  o  i  I^Q  j 

~f  ra  V  AO7/ 

and  equation  (122)  is  changed  to 

I?      O 

(HO) 
(HO 
WT/  +  OS;  +£f)-^(^y+(A  +  £r  y    (I42) 

S)2  (I«) 

(144) 


m  n' 


+ 
mn 


J(^y+(I  +  j_v  j5+(^±i^ 

^v»7      V         OTMV       ~          ^    mn    J 


(145) 


when  ,S  =  i  or  at  synchronism 

i 


mn 


(I46) 


With  an  excessively  large  reluctance  of  the  magnetic  structure 
in  line  with  the  brushes  B^B^  (Fig.  9),  that  is,  with  an  enor- 
mous value  of  m,  the  power  factor  at  synchronous  speed 
approaches 

Cos0=-—  L=  (I47) 

Vl  +  w2 

the  interpretation  of  which  equation  is  that  the  operating  power- 
factor  of  such  a  machine  is  largely  dependent  upon  the  ratio  of 
field  to  armature  turns.  A  little  study  will  show  that  at  any 
chosen  speed,  whether  synchronous  or  not,  the  cotangent  of  the 
angle  of  lag  is  directly  proportional  to  the  ratio  of  armature  to 
field  turns,  and  that  the  power-  factor,  the  corresponding  cosine, 
can  be  given  any  desired  value  by  a  proper  proportioning  of  the 
windings.  This  feature  will  be  treated  more  in  detail  when  deal- 
ing with  compensated  motors. 

The  current  of  the  high  brush-line-reluctance  machine  is 


The  Sibley  Journal  of  Engineering.  55 

,. E En  i 


z    xt    v/^T^^+Ty  (148) 

V     m  n     J 
The  power  is 

£2rc  5  i 

(i49) 


mn     J 

The  torque  is 

=  5  =:  ~X^  '  5,,    ^^2+  iV  =  ~^T  (r5o) 

v     mn    J 
At  starting  the  torque  is 

«  _  ^2^ 

^rwrc2-fiy  (150) 

v — #r« — y 

At  synchronous  speed  the  torque  is 


(152) 


m  n 
which  ratio,  with  an  enormous  value  of  m,  approaches 

g-H^-  ('53) 

the  significance  of  which  is  that  the  change  of  torque  from  stand- 
still to  synchronism  can  be  altered  at  will  by  change  in  the  ratio 
of  field  to  armature  turn  and  that  a  relatively  low  value  of  n 
would  produce  a  machine  suitable  for  traction. 

By  using  projecting  field  poles  thus  leaving  large  air-gaps  in 
the  axial  brush  line  and  thereby  increasing  the  reluctance  of  the 
structure  inline  with  the  magneto- motive  force  of  the  armature  cur- 
rent, the  flux  produced  by  the  armature  current  may  be  materially 
reduced,  thus  giving  to  m  a  relatively  large  value,  and  the  power 
factor  will  be  thereby  correspondingly  increased  with  a  resultant 
improvement  in  the  torque  characteristics  of  the  machine.  Even 
under  the  most  favorable  conditions,  however,  it  is  impossible  to 
reduce  the  reactance  of  the  armature  circuit  to  an  inappreciable 


56  Compensated  Series  Motor. 

value,  that  is,  to  give  to  m  an  enormous  value,  due  to  the  in- 
evitable presence  of  the  magnetic  material  of  the  projecting  poles. 
The  most  satisfactory  method  of  reducing  the  inductive  effect 
of  the  armature  current  is  to  surround  the  revolving  armature 
winding  with  properly  disposed  stationary  conductors  through 


COf*£ 


A 

FiG.  10.     Inductively  Compensated  Series  Motor. 

which  current  flows  equal  in  magneto-motive  force  and  opposite 
in  phase  to  the  current  in  the  armature.  This  compensating 
current  may  be  produced  inductively  by  using  the  stationary 
winding  as  the  short  circuited  secondary  of  a  transformer  of 
which  the  armature  is  the  primary,  as  illustrated  diagram- 
matically  in  Fig.  10,  or  the  main  line  current  may  be  sent  di- 


The  Sibley  Journal  of  Engineering. 


57 


rectly  through  the  compensating  coil  as  shown  in  Fig.  n.  In 
the  former  case  the  transformer  action  is  such  that  the  com- 
pensation is  practically  complete,  giving  minimum  combined 
reactance  of  the  two  circuits  while  in  the  latter  ease,  the  propor- 
tion of  compensation  can  be  varied  at  will.  It  is  found  that  in 
any  case  the  best  general  effects  are  produced  when  the  com- 
pensation is  complete,  and  experiments  seem  to  indicate  that 
under  such  conditions  the  two  methods  of  compensation  differ 

r/ELO    CO/L 


FIELD  CO/L 


FIG.  ii.     Conductively  Compensated  Series  Motor. 

inappreciably   for    strictly   alternating   current  work,    but  that 
for  direct  current  operation  where  the  forced  compensation  can 


58  Compensated  Series  Motor. 

be  used  to  prevent  field  distortion  and  improves  the  commutation, 
the  latter  method  is  preferable. 

Referring  to  Figs.  10  and  n,  assume  an  ideal  series  motor 
with  complete  compensation,  letting  n  be  the  ratio  of  effective 
field  to  armature  turns,  at  any  speed  61  with  synchronism  as  unity, 
the  apparent  impedance  of  the  motor  circuits  will  be 

z=x,  Jj+i  (154) 

of  which 

X-X,  (155) 

represents  the  reactance  of  the  motor  circuits  which  is  confined 
to  the  field  coil,  and  of  which 


represents  the  apparent  resistance  effect  of  the  dyamo  speed 
e.m.f.  counter  generated  at  the  brushes  BVB.L  due  to  the  cutting 
of  the  field  flux  by  the  armature  conductors,  (See  eq.  123). 

The  power  factor  is 


R 
~Z 


~=r=  (157) 


^r  +  I 


which  continually  approaches  positive  or  negative  unity  with  in- 
crease of  speed  in  the  corresponding  direction. 
At  synchronism  when  5  =  i     the  power  factor  is 

cos  0  =  — ss=±==s-  (see  eq.  147)  (158) 

v  i  -|-  n2 

The  line  current  is 

,     E      E     i_ 

^Z^X^-f^  ('59) 

NJF" 

The  power  is 

5 
/>=  EIco$0=  — -  -  _ —  (160) 

The  torque  is 


The  Sibley  Journal  of  Engineering.  59 

r>  772  /2xt^ 

D=  s  =  o  •  =  ~~  (see  eq-  I5o) 


The  ratio  of  the  torque  at  synchronous  speed  to  that  at  stand- 
still is 

D  i  n* 

L  =      ~     -  =        T       (seeeq.  153)  (162) 


which  in  a  practical  machine  can  be  made  as  much  smaller  than 
unity  as  desired  by  a  proper  proportioning  of  the  field  and  arma- 
ture windings.     It  is  evident,  therefore,  that  such  a  machine  can 
be  made  suitable  for  traction  when  a  proper  value  of  n  is  chosen. 
The  above  equations  refer  to  ideal  motors  without  resistance 
and  local  leakage  reactance  and  devoid  of  all  minor  disturbing 
influences.     A  close  approximation  for  the  effect  of  the  resistance 
and  leakage  reactance  may  be  obtained  as  follows  : 
Let  r{  =  resistance  of  field  coil 

rc  =  resistance  of  compensating  coil  (reduced  to  a  i  to  i, 

armature  ratio) 
ra  =  resistance  of  armature 
xt  =  local  reactance  of  field  coil 
x^  =  combined  leakage  reactance  effect  of  armature  and 

compensating  coils. 
Then  the  apparent  impedance  is 


Z=  J(— '+  rr  +  re  +  O'  +  (*,  +  ^  +*J  (  I  63) 

^  v.    n 
Power  factor  is 

SXj+  rl  +  rc  +  r, 
Cos  e=z-= 175^  =  (I64) 


j    (165) 


n 
Power  input  is 


The  copper  loss  and  equivalent  effective  resistance  loss  will  be, 

_  £*(rt+rc  +  rj 

(l66) 


,SX 

(n 


/  v     ?• 

{   UNIVERSITY  j 

ti&r 


60  Compensated  Series  Motor. 

Electrical  output  is 


The  torque  is 

D  /2     D  7"2 

/ 


(167) 


(see  eg.  161)  (168) 


The  equations  here  given  are  represented  graphically  in  the 
diagrams  of  Figs.  10  and  n,  which  show  the  impedance  (e.m.f. 
for  unit  current)  characteristics  of  the  machines. 

OA=r{ 

BC  =  ra  +  rc 

AB  =  Xt  +  *f 


at  speed  5* 
n 

OE  =  Z  at  speed  51 

cos  EOA  =  cos  0  =  power  factor  at  speed  ,5" 
These  characteristics  together  with  the  brush  short  circuiting 
effect  and  other  minor  modifying  influences  will  be  discussed  in 
detail  in  a  later  paper.  It  is  sufficient  here  to  state  that  the  effect 
of  the  short  circuit  by  the  brush  of  a  coil  in  which  an  active  e.m.f. 
is  generated,  both  by  transformer  and  speed  action,  tending  to 
increase  the  apparent  impedance  effects  at  high  speeds  is  to  some 
extent  balanced  by  the  fact  that  the  flux  which  causes  the  gener- 
ation of  a  counter  e.m.f.  by  dynamo  speed  action  is  out  of  phase 
and  lagging  with  respect  to  the  line  current  and  that  tne  counter 
e.m.f.  therefore,  tends  to  lag  behind  the  current  or  to  cause  the 
current  to  become  leading  with  respect  to  the  counter  e.m.f.,  so 
that  the  neglected  disturbing  influences  tend  to  render  the  final 
effect  quite  small,  the  result  being  that  the  incomplete  equations 
and  corresponding  graphical  diagrams  as  given  above,  represent 
quite  closely  the  observed  performance  characteristics  of  the  com- 
pensated series  motors. 


ALTERNATING  CURRENT  COMMUTATOR  MOTORS. 
IV.  INDUCTION-SERIES  MOTOR.* 

BY  A.  s.  M'ALLISTKR. 

Excellent  performance  of  the  conpensated  alternating- current 
motor  may  be  obtained  by  using  the  field  coil  as  the  load  circuit 
from  the  compensating  coil  employed  as  the  secondary  of  a  trans- 
former, the  armature  being  used  as  the  primary,  as  diagrammat- 
ically  represented  in  Fig.  12.  The  current  which  enters  the 


SPEED       EMF 


FIG.  12.  Induction-Series  Motor. 


*  Thesis  for  Ph.D.  degree,  Cornell  University. 


62  The  Sibley  Journal  of  Engineering. 

armature  winding  through  the  brushes  Bl  £2  causes  the  formation 
on  the  armature  core  of  magnetic  poles  having  the  mechanical 
direction  of  the  axial  line  joining  the  brushes,  and  the  rate  of 
change  of  the  magnetism  generates  an  electromotive  force  in  the 
compensating  coil.  Due  to  this  electromotive  force,  current 
flows  through  the  locally-closed  circuits  around  the  compensat- 
ing and  field  coils,  and  produces  magnetic  poles  in  the  stationary 
field- cores. 

Consider  now  the  load-circuit  surrounding  the  quadrature 
field-cores.  Since  to  this  winding  there  is  no  opposing  secondary 
circuit,  the  magnetism  in  the  core  will  be  practically  in  time- 
phase  with  the  current  producing  it.  This  current  is  the  second- 
ary load- current  of  the  transformer.  As  is  true  in  any  trans- 
former, there  will  flow  in  the  primary  coil  a  current  in  phase  op- 
position to  the  secondary  current  in  addition  to  and  superposed 
upon  the  primary  no-load  exciting-current.  It  is  thus  seen,  that 
the  load- current  in  the  primary  (or  armature)  coil  will  be  in 
time-phase  opposition  with  the  magnetism  in  the  quadrature  core. 
And,  since  this  current  and  the  magnetism  reverse  signs  together, 
the  torque,  due  to  their  product  and  relative  mechanical  position, 
will  remain  always  of  the  same  sign — though  fluctuating  in  value. 
Hence  the  machine  operates  similarly  to  a  direct- current  series 
motor. 

When  the  armature  revolves  at  a  certain  speed,  the  motion 
of  its  conductors  through  the  quadrature  magnetic  field,  generates 
in  the  armature  winding  an  electromotive  force  which  appears  at 
the  brushes  Bl  B2  as  a  counter  e.m.f.  This  weakens  the  effec- 
tive electromotive  force  and  therewith  the  armature- current,  the 
armature-core  magnetism,  the  field-current  and  the  field-core 
magnetism.  Thus  there  results  from  increased  speed  of  the  arm- 
ature a  reduced  torque,  just  as  occurs  in  direct-current  series 
motors.  By  increasing  the  applied  electromotive  force,  an  in- 
crease of  torque  can  be  obtained  even  at  excessively  high  speeds, 
and  the  motor  tends  to  increase  indefinitely  the  speed  of  its  arm- 
ature as  the  applied  electromotive  force  is  increased,  or  as  the 
counter  torque  is  decreased.  There  is  no  tendency  to  attain  a 
definite  limiting  speed  as  is  found  to  be  true  with  revolving 
field  induction-motors  and  repulsion  motors. 

Let  E&  be  the  counter  transformer  e.m.f.  across  the  armature 
coil,  the  armature  being  stationary. 


Induction-  Series  Motor.  63 

Then 

~  2  7T  /  '  N    <£  f        \ 

E*  =  —  ,-    a8a>  see  eq.  (55)  (169) 

V  2    IO 

where  /"  =  frequency  in  cycles  per  second 

N&  =  effective  number  of  armature  turns 
<£a  =  maximum  value  of  armature  flux  cutting  the 
compensating  coil 

^/a  =  -  seeeq.  (56)  (170) 

2  7T 

where  C  is  the  actual  number  of  conductors  on  the  armature,  a 
bipolar  model  being  assumed. 

t«70 


Let  NQ  =  effective  number  of  turns  on  the  compensating  coil, 

4- 

where  /sc  =  transformer  e.m.f.  of  the  compensating  coil. 
Let  Nt  =  effective  number  of  turns  on  the  field  coil 


then  £t=-'-  (173) 

V  2    IO 

where  Et  =  impre,ssed  e.m.f.  of  the  field  coil 

<£f  =  maximum  value  of  field  flux 

Et  =  E0,  hence  N0  <t>&  =  N,  ^  (  1  74) 

and 

^  =  §  C'75) 

^>a  ^f 

Let  ^"v  be  the  e.m.f.  counter  generated  at  the  brushes  B^  B^ 
(Fig.  12)  by  speed  action  due  to  the  cutting  of  the  flux  <£f  by  the 
armature  conductors  C  at  speed  V  revolutions  per  second,  then 

£'-£££          seeeq.  (59)  (176) 

V-  Sf  (177) 

where  5*  is  the  speed  with  synchronism  as  unity. 
Combining  (171),  (176)  and  (177) 

*t  =  ^=^  (I78) 

Let  n  be  the  ratio  of  effective  field  to  compensating  coil  turns. 

o   r? 

£v  =  --  -a  seeeq.  (123)  (179) 

n 


64  The  Sibley  Journal  of  Engineering. 

This  electromotive  force  is  in  time-phase  with  the  field  flux 
<j>f,  is  in  phase  opposition  with  the  live  current  and  hence  is  in 
time  quadrature  (leading)  with  respect  to  the  e.m.f.  E&.  The 
impressed  electromotive  force  E  is  balanced  by  the  two  com- 
ponents, Ev  and  E&  so  that 

+  E*  (180) 


-E     W 

*\^> 


+  i  (181) 


On  the  basis  of  unit  line  current,  the  electro-motive  forces  may 
be  treated  as  impedances,  as  was  done  with  the  repulsion-series 
and  compensated-series  motors. 


where  =  R  and  Xt  =  x 

n 

Xt  being  the  combined  reactance  effect  of  the  field,  compensating 
coil  and  armature  circuits. 
The  power  factor  is, 

5 

R  ___  *L=  S  (I83) 

cos0=Z~  ~ 


which  when  6*  =  i  or  at  synchronism,  reduces  to 


the  interpretation  of  which  is  that  the  power  factor  at  synchro- 
nism can  be  caused  to  approach  unity  quite  closely  by  the  use  of 
a  small  value  of  n,  that  is,  by  employing  a  small  ratio  of  field  to 
compensating  coil  turns.  With  increase  of  speed  the  power  fac- 
tor continually  increases  for  any  value  of  n. 
The  line  current  is 


The  power  is 

5 


n  n 

_^_^__^      (I86) 


Induction-Series  Motor.  65 

which  becomes  negative  when  S  reverses,  or  the  machine  oper- 
ates as  a  generator  when  driven  against  its  natural  tendancy  to 
rotation. 

The  torque  is 

D=5~xt(s*  +  n>)  =  ^ir          (l8y) 

which  is  maximum  at  maximum  current  and  retains  its  sign 
when  >S  is  reversed. 

At  starting,  the  torque  is 

77*          <yt 

D0  =  ^-'-  (188) 

Xt     n 

at  synchronous  speed,  the  torque  is 

^  "§.'(!+«')  (I89) 

and 

t  =  rr^  (I90) 

which  when  n  =  i  reduces  to 

^  =  -4— =-5  (i9O 


and  can  be  given  any  desired  value  by  a  proper  selection  of  n, 
see  eq.  (153).  A  relatively  low  value  of  n  would  produce  a 
machine  having  the  torque  characteristics  of  the  direct  current 
series  motor  and  hence  one  suitable  for  traction.  See  eq.  (162). 

It  remains  to  investigate  the  relation  of  the  currents  in  the 
compensating  coil  and  in  the  armature  circuit  (the  secondary  and 
primary  of  the  assumed  transformer. ) 

Let  i&  be  the  current  which  would  flow  in  the  armature  when 
the  field  coil  circuit  is  open.  Then  z'a  is  the  exciting  current  of  the 
assumed  transformer  and  it  has  a  value  such  that  its  product  with 
the  effective  number  of  armature  turns,  forces  the  flux,  <£a, 
demanded  by  the  impressed  e.m.f.,  through  the  reluctance  of 
their  paths  in  the  magnetic  structure,  in  line  with  the  brushes 
Bl  B^  (Fig.  12).  When  the  field  circuit  is  closed  there  flows 
through  the  field  and  compensating  coil  a  current  zf,  of  a  value 
such  that  its  magnetomotive  force  when  flowing  through  the  field 
turns  Nv  produces  the  flux  <£f  demanded  by  the  e.m.f.  E^  or  EG. 
The  current  it  is  in  time- phase  with  the  flux  <f>t  and  hence  is  in 
time  quadrature  with  the  e.m.f.  EG,  The  current  za  is  in  phase 
with  the  flux  <£a  and  in  time  quadrature  with  E&  or  Ec.  When 
the  field  circuit  is  closed  a  current  equal  in  magnetomotive  force 


66  The  Sibley  Journal  of  Engineering. 

and  opposite  in  phase  to  it  is  superposed  upon  za  in  the  primary 
(armature)  circuit.  These  two  currents  are  directly  in  phase  so 
that  the  resultant  current  becomes 

/=4+M  (192) 

where  p  is  a  proportionality  constant  the  value  of  which  will  be 
discussed  later. 

Since  both  i&  and  it  reach  their  maximum  values  simultaneously 
with  <£f,  one  is  led  to  the  highly  interesting  conclusion  that  even 
the  exciting  current  i&  is  effective  in  producing  torque  by  its 
direct  product  with  the  field  magnetism,  and,  that  under  speed 
conditions  both  z"a  and  p  it  are  equally  effective  (per  ampere)  in 
producing  power. 

The  relative  values  of  /a  and  it  and  of  p  may  be  approximated 
as  follows  : 

Assuming  similar  conditions  for  the  three  coils,  the  field,  the 
compensating  and  the  armature  circuits, — equal  reluctance — 

/  N       LN, 

_J^_S  =   J_f  (I93) 

<Pa  9f 

N,=  nNG  (194) 

N*$*  =  Nt$t      seeeq.  (174)      (195) 

*f=a  d96) 


From  transformer  relations  there  is  obtained  the  equation 

— j=p  seeeq.  (192)  (198) 

Combining  (197)  and  (198) 

*r=T^i  ('99) 

Combining  (199)  and  (192) 

/=  ^a(:  +  ^r)  (20°) 

Comparing  (199)  and  (200), 

*;  =  __^  = £_  (201) 


T       _1_        * 

•*•       I          n 


The  relations  above  expressed  depend  upon  certain  assump- 
tions as  to  the  reluctance  in  line  with  the  armature  circuit  and 


Induction-  Series  Motor.  67 

the  field  coil,  and  will  be  modified  if  the  assumptions  made  are 
not  applicable  to  the  motor  as  constructed.  As  a  method  of  re- 
viewing the  problem,  in  a  general  way,  however,  the  assumption 
made  and  the  conclusions  drawn  therefrom  are  sufficiently  exact. 
In  the  determination  of  the  equations  used  above,  an  ideal  motor 
has  been  considered,  the  resistance  and  local  leakage  reactance 
effects  being  neglected.  Actual  operating  conditions  may  be 
more  closely  represented  as  follows  : 

Let 

rt  =  resistance  of  field  coil. 

rc  =  resistance  of  compensating  coil. 

ra  =  resistance  of  armature. 

xt  =  local  leakage  reactance  of  field  coil. 

xc  =  local  leakage  reactance  of  compensating  coil. 

xt  =  local  leakage  reactance  of  armature  circuit. 
Then  the  copper  loss  of  the  motor  circuits  will  be 

P  *m  =  /V.  +  if  (r,  +  O  =  P  [r.  +          t]     (2O2) 


where  Rm  is  the  effective  equivalent  value  of  the  motor-circuit 
resistance,  that  is, 

(203) 


Similarly  it  may  be  shown  that  the  equivalent  effective  value 
of  the  local  leakage  reactance  of  the  motor-  circuit  is 


Combining  equations  (182),   (203),  and  (204),  the  apparent 
impedance  of  the  motor-  circuits  becomes 


(205) 

The  power  factor  is 


R=  _ 

C°  r'+r' 


Z  +r 

r        r^          n 

(206) 
The  current  is  —  =  7.  (207) 


68  The  Sibley  Journal  of  Engineering. 

The  input  =  El  cos  6.  (  208  ) 

The  output  is  P=  El  cos  6  —  PRm.  (209) 


/>= 


. 

The  torque  is 

see  eq.  (187)  andeq.  (168)      (212) 


>j  n 

The  graphical  diagram  of  Fig.   12.    represents   the   above  im- 
pedance equations,  (e.m.f.  for  unit  current),  where 


(2I4) 

(215) 


O  F=  Zat  speed  5  (216) 

cos  F  O  A  =  cos  0  =  power  factor  at  speed  5     (217) 

AlthouglTneglecting  certain  modifying  eifects,  the  graphical 
diagram  represents  quite  closely  the  observed  performance  char- 
acteristics of  the  induction-series  motor.  An  inspection  of  equa- 
tion (205)  will  show  that  certain  values  there  given  may  be 
represented  by  others  of  much  simplified  nature  since  various 
terms  there  contained  are  constant  in  any  chosen  motor. 

Let,  therefore 


P  =  ±-<  (220) 

n 


Induction-  Series  Motor.  69 

then  the  apparent  impedance  becomes, 

Z=*  \/(X  +  PS)*  +  X*  (221) 

the  power  factor  is, 


which  continually  approaches  unity  with  increase  of  speed. 

Let  rotation  of  the  armature  in  the  direction  produced  by  the 
electrical  (its  own)  torque  be  considered  positive.  Then  may 
rotation  in  the  contrary  direction  (against  its  own  torque)  be 
considered  negative.  Since  the  power  component  of  the  motor 
impedance  has  a  certain  value  at  zero  speed,  and  increases  with 
increase  of  speed,  it  should  follow  that  by  driving  the  rotor  in  a 
negative  direction  the  apparent  power  component  will  reduce  to 
zero  and  disappear.  The  power  factor  then  reduces  to  zero  and 
the  current  supplied  to  the  motor  will  represent  no  energy  flow- 
ing either  to  or  from  the  motor. 

This  will  be  apparent  from  the  relations  above  set  forth,  as 
well  as  by  the  relations  algebraically  expressed  by  the  equation 

-       power  - 

the  negative  sign  being  due  to  the  direction  of  rotation  and  the 
expression  reducing  to  zero  for  zero  value  of  the  apparent  power 
component  J^  —  PS.  A  further  increase  of  speed  in  the  nega- 
tive direction  will  cause  the  expression  for  the  power-  factor  and 
for  the  power,  to  become  negative,  the  interpretation  of  which  is 
that  the  machine  is  now  being  operated  as  a  generator  and 
hence  is  supplying  energy  to  the  line,  that  is,  energy  is  flowing 
from  the  machine.  Fig.  13,  which  gives  the  observed  perform- 
ance characteristics  of  a  certain  induction-series  motor,  will 
serve  to  show  to  what  extent  these  theoretical  deductions  may 
be  realized  in  an  actual  machine.  If,  then,  during  operation  as 
a  motor  at  a  certain  speed,  the  quadrature  field  flux  be  relatively 
reversed  with  reference  to  the  brush  axial-line  field  flux,  so  as  to 
tend  to  drive  the  armature  in  the  opposite  direction,  not  only 
will  a  braking  effect  be  produced  by  such  change  but  energy 
will  be  transmitted  from  the  machine  to  the  line. 

The  effect  of  the  short  circuit  by  the  brush  of  a  coil  in  which 
an  active  e.m.f.  is  generated,  which  has  been  omitted  in  the 
above  equation's,  though  completely  included  in  the  test  curves, 


The  Sibley  Journal  of  Engineering. 


may  be  treated  as  follows.  Referring  to  Fig.  12  it  will  be  seen 
that  at  any  speed  6"  there  will  be  generated  in  the  coil  under  the 
brush  by  dynamo  speed  action  an  e.m.f. 

see  eq.  (43)          (224) 


FiG.  13.  Test  Characteristics  of  Induction-Series  Motor. 

where  A" is  constant.  This  e.m.f.  is  in  time-phase  with  the  flux 
<£a.  In  this  coil  there  will  also  be  generated  an  e.m.f.,  <?f,  by 
the  transformer  action  of  the  field  flux,  such  that 

ef=K<t>t         seeeq.  (44)          (225) 

This  e.m.f.  is  in  time  quadrature  to  <£r  Since  <£{  and  <£a  are  in 
time  phase,  the  component  e.m.f.'s  acting  in  the  coil  under  the 
brush  are  in  time  quadrature,  so  that  the  resultant  e.m.f.  is 

$+tf  (226) 

see  eq.  (175)  (227) 


*.-» 


S'  +  A 


combining  equations  (169)  and  (181) 
.g-g'/AT.*. 

\/2  •   I08 


(228) 


(229) 


Induction- Series  Motor.  71 


combining  (230)  and  (228) 

p=^  (231) 

'•ji  (232) 


where  A  is  a  constant  as  found  above. 

When  n=  i,  £b  is  constant,  independent  of  the  speed,  while 
when  ?z  is  very  small  E^  is  large  at  zero  speed  and  continually 
decreases  with  increase  of  speed.  When  6"=  i  or  at  synchronous 
speed 


quite  independent  of  the  value  of  n. 

The  relative  impedance  effect  of  E^  can  be  determined  by  com- 
bining equations  (232)  and  (185)  thus 


+1  (235) 

B  being  a  constant.  The  interpretation  of  equation  (235)  is 
that  the  apparent  impedance  effect  of  the  short  circuit  by  the 
brush,  consists  of  two  components  in  quadrature,  one  component 
being  of  constant  value  and  the  other  varying  directly  with  the 
speed.  Experimental  observations  fully  confirm  these  theoreti- 
cal conclusions,  and  show  that  the  increase  in  apparent  reactive 
effect  with  increase  of  speed  for  motor  operation  is  approxi- 
mately counterbalanced  by  the  lagging  counter  e.m.f.  (leading, 
current)  effect  of  the  time-phase  displacement  between  exciting 
current  and  field  magnetism  as  has  been  mentioned  previously 
and  as  will  be  dwelt  upon  subsequently.  During  generator 
operation,  that  is,  with  negative  value  of  S,  the  apparent  re- 
active effect  of  the  short  circuit  at  the  brush  adds  directly  to 
the  lagging  field  flux,  counter  e.m.f.  effect  and  therefore,  the 


72  The  Sibley  Journal  of  Engineering. 

apparent  reactance  of  the  motor  circuits  increases  rapidly  with 
increase  of  speed  in  the  negative  direction,  though  remaining 
practically  constant  for  all  values  of  positive  speed.  These  facts 
will  be  appreciated  from  a  study  of  the  test  characteristics  of  the 
induction  series  machine  throughout  both  its  generator  and 
motor  operating  range  as  shown  in  Fig.  13. 

Mention  has  frequently  been  made  of  the  fact  that  in  the 
development  of  the  equations  for  expressing  the  performance  of 
the  various  types  of  series  motors  the  effect  of  the  hysteretic 
angle  of  time-phase  displacement,  between  the  magnetizing  force 
and  the  magnetism  produced  thereby  has  been  neglected.  In  a 
closed  magnet  path  operated  at  a  density  below  saturation  the 
tangent  of  the  angle  of  time-  phase  displacement  will  be  approxi- 
mately unity  —  depending  for  its  exact  value  upon  the  quality  of 
the  magnetic  material.  Consider  the  magnetic  and  electric 
circuits  of  the  machine  treated  as  a  stationary  transformer. 
The  hysteresis  loss  will  be,  in  watts, 


where  A  =  cross  sectional  area  of  magnetic  path 

/  =  length  of  magnetic  path  (in  centimeters) 
Bm  —  maximum  magnetic  density  (c.g.s) 

The  electromotive  force  counter  generated  in  the  transformer 
coil  having  N  turns  will  be,  in  effective  volts, 

E=  :    (237) 


The  current  to  supply  the  hysteresis  loss  will  be 


With  a  permeability  of  /A  the  magnetizing  .component  of  the 
no-load  current  will  be 

/,--^L£^-      «U.5J  (239) 


10 

For  a  certain  value  of  permeability,  depending  upon  the  mag- 
netic density,  the  hysteresis  current  and  the  magnetizing  current 
become  equal  in  value.  Thus  when  the  two  components  of  the 
no-load  exciting  current  become  equal  //*  =  7h, 

.002  1  /^'6  ^-/-IO  (  ^ 

(24°' 


Induction-  Series  Motor.  73 

from  which  is  obtained, 

/x=  119  B^  (250) 

The  meaning  of  equation  (250)  is  that  with  a  permeability  of 
the  value  there  designated,  the  hysteresis  current  and  the  no-load 
exciting  current  are  equal  in  value  and  that  the  resultant  current 
\X/h2  _j_  7^2  is  displaced  from  the  flux  by  a  time-phase  angle  whose 
tangent  (equal  at  all  times  to  the  ratio  of  7/x,  to  7h)  is  unity,  as 
stated  previously.  For  commercial  laminated  steel  operated  at 
densities  below  saturation,  the  permeability  differs  but  slightly 
from  the  value  given  by  the  equation  (250),  though  with  increase 
of  magnetic  density  above  7,000  lines  per  square  centimeter  the 
permeability  falls  off  rapidly  and  the  tangent  of  the  angle  of  dis- 
placement between  flux  and  current  becomes  correspondingly 
increased. 

In  an  open  magnetic  circuit  the  permeability  of  a  portion  of 
the  path  reduces  from  the  value  approximately  represented  by 
the  equation  (250)  to  a  value  of  unity,  producing  a  very  marked 
effect  upon  the  hysteretic  angle  of  displacement  between  flux 
and  current. 

Let  /  =  length  of  path  in  magnetic  material  of  permeability  /*, 

d=  length  of  path  in  air, 

then,  assuming  that  permeability  is  as  represented  by  equation 
(250),  the  tangent  of  the  angle  of  time-phase  displacement  be- 
tween flux  and  magnetizing  force  is  such  that 


(251) 


the  significance  of  which  equation  is  that  the  flux  lags  behind 
the  current  producing  it,  by  an  angle  which  depends  for  its  value 
largely  upon  the  ratio  of  the  air-gap  to  the  length  of  the  mag- 
netic path.  Assigning  values  to  /A,  /  and  d,  it  will  be  seen  that 
in  any  practical  case  the  angle  8  must  be  quite  small,  —  seldom 
more  than  2  degrees. 

It  should  be  carefully  noted  that  a  slight  error  is  introduced 
on  account  of  the  fact  that  the  permeability  of  commercial  mag- 
netic material  undergoes  a  cyclic  change  with  each  alternation  of 
the  current,  and  that,  independent  of  the  angle  of  time-phase 
displacement  between  flux  and  current,  the  shape  of  the  waves 
representing  the  time-  values  of  the  two  can  not  both  be  sinu- 
soidal, and  that  in  assigning  a  value  to  the  angle  of  time-phase 


74  The  Sibley  Journal  of  Engineering. 

displacement  between  the  flux  and  current,  the  lack  of  similarity 
of  the  two  waves  has  been  neglected. 

Under  speed  conditions  the  e.m.f.  counter  generated  by  the 
cutting  of  the  armature  conductors  across  the  field  magnetism, 
varies  in  value  with  the  magnetism,  and  hence  it  must  have  a 
wave  shape  of  time- value  similar  in  all  respects  to  that  of  the 
field  flux,  and  must  have  a  time-phase  position  with  reference  to 
the  field  current  quite  the  same  as  that  of  the  magnetism.  The 
counter  generated  speed  e.m.f.  must,  therefore,  lag  behind  the 
current  by  an  angle  whose  tangent  is  as  given  by  equation  (251 ). 
Now  since  the  counter  e.m.f.  lags  behind  the  current,  the  cur- 
rent must  lead  the  counter  e.m.f.  by  the  same  angle — a  fact 
which  has  been  mentioned  previously. 

With  motors  having  air-gaps  of  sizes  demanded  by  mechanical 
clearance,  the  inherent  angle  of  lead  is  quite  small,  and  its  effect 
upon  the  power- factor  is  neutralized  by  the  effect  of  the  short 
circuit  by  the  brush  of  a  coil  in  which  is  generated  an  e.m.f.  by 
both  transformer  and  speed  action  when  the  machine  is  operated 
as  a  motor.  When  the  machine  is  operated  as  a  generator,  how- 
ever, the  hysteretic  angle  and  the  angle  due  to  the  short  circuit- 
ing effect  are  in  a  direction  such  as  to  be  additive  to  the  station- 
ary reactive  effect  of  the  motor  circuits  and,  therefore,  during 
generator  operation  the  power  factor  is  lower  than  during  motor 
operation  as  shown  in  Fig.  13. 

While  the  angle  of  lead  due  to  the  hysteretic  effect,  even  when 
the  machine  is  running  as  a  motor,  is  in  any  case  quite  small  and 
its  good  effects  cannot  be  availed  of,  it  is  possible  by  means  of 
certain  auxiliary  circuits  to  give  to  the  angle  of  time-phase  dis- 
placement between  the  line  current  and  the  flux  any  value  de- 
sired, and  thus  to  cause  the  operating  power  factor  to  become 
unity  or  to  decrease  with  leading  wattless  current,  as  is  shown 
below. 

Fig.  14  represents  diagrammatically  the  circuits  of  a  conduc- 
tively  compensated-series  motor  in  parallel  with  the  field  coil  of 
which  is  placed  a  non-inductive  resistance.  Consider  first,  ideal 
conditions  in  which  the  armature  and  compensating  coils  are 
without  resistance  and  the  compensation  is  complete  so  that  these 
two  circuits,  treated  as  one,  are  without  inductance.  The  field 
coil  is  without  resistance  but  constitutes  the  reactive  portion  of 
the  motor  circuits. 

When  the  armature  is  stationary  the  circuit  through  the  resis- 


Induction- Series  Motor. 


75 


tance  being  open,  the  current  taken  by  the  machine  has  a  value 
determined  by  the  ratio  of  the  impressed  e.m.f.  and  the  reactance 
of  the  field  coil.  This  current  lags  90  time  degrees  behind  the 
e.m.f.  across  the  field  coils.  When  a  resistance  is  placed  in  shunt 
to  the  field  coil,  current  flows  therethrough,  quite  independently 
of  the  field  current.  The  current  taken  by  the  resistance  is  in 
time-phase  with  the  e.m.f.  impressed  upon  the  field  coil. 

COMPENSATING    COIL 


£a  »    SPEED    CM/: 


FIG.  14.— Compensated  Series  Motor  with  Shunted  Field  Coil. 


76  The  Sibley  Journal  of  Engineering. 

In  Fig.  14  let  O  7=  7f  represent  the  field  current,  assumed 
always  of  unit  value.  O  D  =  Et  is  the  e.  m.  f .  impressed  across 
the  field  coil  and  the  shunted  resistance.  7r  is  the  current  taken 
by  the  resistance.  <9C=7,  the  current  which  flows  through 
the  armature  and  compensating  coil  or  the  resultant  current  taken 
by  the  motor  has  a  value  represented  by  the  equation 

7=v/7f2  +  7r2  (252) 

and  has  a  phase  displacement  /3  with  reference  to  the  field  current 
such  that 

tan£  =  y  (253) 

With  unit  value  of  field  current,  under  speed  conditions,  the 
e.m.f.,  Es,  (DjFoi  Fig.  14)  counter  generated  at  the  brushes, 
due  to  the  presence  of  the  field  flux,  will  be  proportional  directly 
to  the  speed  and  in  time-phase  with  the  field  current.  Thus  this 
component  of  the  counter  e.m.f.  of  the  motor  is  in  no  wise 
affected  by  the  presence  of  the  current  through  the  shunted 
resistance.  At  a  certain  speed,  the  counter  generated  armature 
e.m.f.  will  have  a  value  represented  by  the  line  D  F  Fig.  14  the 
resultant  e.m.f.  E  —  OF  being  the  vector  (quadrature)  sum  of 
the  speed  e.m.f.  and  the  stationary  e.m.f.  Ea  that  is 

E  =  VEl  +  E*  (254) 

and  has  a  time-phase  a  position  with  reference  to  the  speed  e.m.f. 
Es  such  that 

tana  =  ^f  (255) 

An  inspection  of  Fig.  14  will  show  that  under  operating  condi- 
tions, the  angle  of  time-phase  displacement  between  the  current 
and  the  electromotive  force,  0,  has  a  value  represented  by  the 
equation 

0=P  —  a  (256) 

or  the  current  leads  the  e.m.f.  by  the  angle  0.  At  a  certain 
critical  speed  for  each  value  of  shunted  resistance,  or  at  a  certain 
value  of  resistance  for  any  given  speed,  the  angle  0  reduces  ta 
zero,  and  the  power  factor  of  the  motor  becomes  unity. 

It  is  interesting  to  observe  the  effect  of  removing  the  resistance 
from  in  shunt  with  the  field  circuit.  Since  the  current  taken  by 
the  resistance  is  90  time-degrees  from  the  field  flux,  the  resultant 
torque  due  to  the  product  of  this  component  of  the  current  and 
the  flux  is  of  zero  value,  the  instantaneous  torque  alternat- 


Induction- Series  Motor.  77 

ing  at  double  the  circuit  frequency.  The  current  through  the 
resistance,  therefore,  contributes  in  no  way  to  the  power  of  the 
machine  or  to  the  counter- generated,  armature-speed  e.m.f.,  and 
when  the  circuit  through  the  resistance  is  opened  no  effect  what- 
soever is  produced  upon  the  value  of  the  current  taken  by  the 
field  coil,  the  counter  e.m.f.  or  the  torque  of  the  machine.  It 
is  apparent,  therefore,  that  the  use  of  the  shunted  resistance  in- 
creases the  circuit  current  in  a  certain  definite  proportion,  the 
added  component  being  a  leading  { '  wattless  ' '  current  under 
speed  conditions.  If  a  reactance  be  placed  in  parallel  with  the 
field  coil,  the  current  which  flows  therethrough  will  be  in  time- 
phase  with  the  field  flux,  and  the  torque  produced  thereby  will 
add  to  the  torque  due  to  the  field  current  and  it  will  affect 
directly  the  whole  performance  of  the  machine.  The  current 
taken  by  a  condensance  in  shunt  with  the  field  coil  will  be  in 
time-phase  opposition  to  the  field  current  and  will  tend  to 
decrease  directly  both  the  circuit  current  and  the  armature 
torque.  An  excess  of  condensance  will  cause  the  torque  to 
reverse  and  the  machine  to  act  as  a  generator  even  when  the 
speed  is  in  a  positive  direction.  When  the  condensance  and  the 
field  reactance  are  just  equal,  the  circuit  current  reduces  to  zero 
and  the  torque  disappears.  Under  the  conditions  here  assumed, 
the  counter  generated  e.m.f.  at  the  armature  remains  propor- 
tional to  the  product  of  the  field  flux  and  the  speed,  and  there 
appears  the  remarkable  combination  of  zero  current  being  trans- 
mitted over  a  certain  counter  e.m.f.  (that  is,  through  infinite 
impedance)  to  divide  into  definite  active  currents  at  the  end  of 
the  transmission  circuits. 

From  what  has  been  demonstrated  above,  it  is  seen  that 
shunted  condensance  acts  to  take  current  in  phase  opposition  and 
to  decrease  the  torque  ;  reactance  takes  current  directly  in 
phase,  and  increases  the  torque,  while  resistance  takes  current 
in  leading  quadratures  with  the  field  current  and  has  no  effect 
upon  the  torque.  It  is  evident  that  the  improvement  in  power 
factor  due  to  the  use  of  the  resistance  is  advantageous  provided 
the  losses  caused  by  the  resistance  are  not  excessive.  Referring 
to  Fig.  14,  when  the  resistance  is  not  used  the  power  taken  by 
the  machine  under  speed  conditions  is 

/>=  <9/.0/^cosJro/=/f^cosa  =  /f£;  (257) 

When  the  machine  is  stationary,  the  power  absorbed  by  the 
resistance  is 

IrEt  (258) 


7 8  The  Sibley  Journal  of  Engineering. 

When  the  motor  is  running  with  shunted  field  coil,  the  power 
delivered  to  the  machine  is 

/>  =  OC-  OF- cos  COF=  IE  cos  6  (259) 

0  =  ft-a  (250) 

cos  0  =  cos  ft  cos  a  +  sin  ft  sin  a  (261 ) 

Pt  =  /cos  ft'E  cos  a  -f-  /sin  ft>E  sin  a  (262) 

The  significance  of  equation  (263)  is  that  the  energy  absorbed 
is  that  incident  to  the  use  of  the  resistance,  and  that  for  a  given 
current  it  is  unaffected  by  the  speed  e.m.f.  Thus  the  current 
taken  by  the  resistance  multiplies  into  the  stationary  transformer 
e.m.f.  to  give  the  actual  watts  absorbed  while  the  same  current 
multiplies  into  the  speed  e.m.f.  to  give  apparent  leading  wattless 
power. 


CURRENT  234-5 

FlG.  15.  Observed  E.M.F. — Current  Characteristics  of  Plain  Series  Motor 
with  Shunted  Field. 

In  the  derivation  of  the  above  equations  ideal  conditions  have 
been  assumed,  which  cannot  be  obtained  in  a  practical  motor, 
motor.  Fig.  15  represents  the  observed  e.m.f.  current  charac- 
teristics of  a  certain  plain,  uniform  reluctance  motor  (see  Fig.  9) 
with  shunted  field  coils,  and  serves  to  show  that  even  such  an 
unfavorable  machine  may  be  caused  to  operate  at  unity  power 
factor  at  any  speed  greater  than  about  one-half  synchronism. 


APPENDIX. 


In  compliance  with  the  request  of  the  committee  having  in  charge  the 
work  of  the  candidate,  there  is  given  below  a  list  of  articles  dealing 
with  alternating- current  phenomena  as  published  by  him  during  his  candi- 
dacy for  the  degree  of  Doctor  of  Philosophy,  at  Cornell  University. 

Frequency  Converters.     Elec.  W.  and  Eng.    May  n,  1901. 

The  Regulation  of  Alternating  Current  Generators.    Amer.  Elec.  Aug.,  1901. 

Parallel  Operation  of  Alternators.     Amer.  Elec.    Sept.,  1901. 

Transformers.     Amer.  Elec.     Oct.,  1901. 

Measurement  of  the  Angle  of  Lag  of  Three-Phase  Circuits  with  One  Watt- 
meter. Elec.  W.  and  Eng.  Nov.  23,  1901. 

Rotary  Converters.     Amer.  Elec.     Dec.,  1901. 

Complete  Commercial  test  of  Polyphase  Induction  Motors  Using  One  Watt- 
meter and  One  Voltmeter.  Elec.  W.  and  Eng.  Jan.  n,  1902. 

Measuring  Three-Phase  Circuits.     Elec.  W.  and  Eng.     March  8,  1902. 

Characteristic  Performance  of  the  Induction  Motor.  Amer.  Elec.  April,  1902. 

The  Constant-Current  Transformer.     Amer.  Elec.    May,  1902. 

The  Single-Phase  Induction  Motor.     Amer.  Elec.     June,  1902. 

Characteristic  Performance  of  Alternators.  Trans.  Cornell  Elec.  Society. 
1901-02. 

Polyphase  Induction  Motors  Operating  on  Single- Phase  Circuits.  Amer. 
Elec.  Aug.,  1902. 

Synchronous  Commutating  Machines.     Amer.  Elec.     Oct.  and  Nov.,  1902. 

An  Asynchronous  Motor  with  Unity  Power- Factor.  Sibley  Journal.  Nov. , 
1902. 

Six-Phase  Transformation.     Amer.  Elec.     Dec.,  1902. 

Three-Phase  Measurements.     Elec.  W.  and  Eng.     Dec.  13,  1902. 

Excitation  of  Asynchronous  Generators  by  Means  of  Static  Condensance. 
Elec.  W.  and  Eng.  Jan.  17,  1903. 

Action  of  a  Shunt- Wound  Motor  when  Driven  by  a  Series- Wound  Dynamo. 
Amer.  Elec.  Feb.,  1903. 

Some  Engineering  Features  of  the  Bedell  System  of  Composite  Transmis- 
sion. Elec.  W.  and  Eng.  Feb.  28,  1903. 

The  Joint  Transmission  of  Different  Currents — Bedell  System.  Elec.  Age. 
March,  1903. 

The  Bedell  System  of  Composite  Transmission.  Elec.  Review.  March  14, 
1903. 

Circuits  for  the  Transmission  and  Distribution  of  Electrical  Energy.  Amer. 
Elec.  April,  1903. 

System  for  the  Joint  Transmission  of  Differing  Currents.  Mill  Owners. 
April,  1903. 

Graphic  Representation  of  Induction  Motor  Phenomena.  Trans.  Cornell 
Elec.  Soc..  1903. 

The  Heyland  Asynchronous  Motor.     Elec.  Age.     June,  1903. 

The  Heyland  Induction  Motor.     Amer.  Elec.     July,  1903. 

Asynchronous  Generators.     Amer.  Elec.     Nov.,  1903. 


2  Appendix. 

The  Winter- Eichberg  Single-Phase  Railway  System.  Elec.  W.  and  Eng. 
Dec.  19,  1903. 

Single-Phase  Railway  Motors.     Elec.  W.  and  Eng.     Feb.  13,  1904. 

Alternating-Current  Railway  Motors.  Trans.  Amer.  Inst.  Elec.  Eng.  Feb., 
1904. 

A  Convenient  and  Economical  Electrical  Method  for  Determining  Mechani- 
cal Torque.  Elec.  W.  and  Eng.  May  7,  1904. 

Single-Phase  Induction  Motors.     Trans.  Amer.  I.  E.  E.,  June,  1904. 

Self  Exciting  Asynchronous  Generators.     Trans.  Cornell  Elec.  Soc.    1903-04. 

Efficiency  Curves  of  Rotary  Converters.     Elec.  W.  and  Eng.     June  4,  1904. 

The  Repulsion  Motor.     Amer.  Elec.     Sept.,  1904. 

Single-Phase  Railway  Motors      Elec.  W.  and  Eng.    Nov.  12.1904. 

The  Graphic  Treatment  of  the  Phenomena  of  Static  Transformers  and  In- 
duction Motors.  Sibley  Journal,  Nov.,  1904. 

Electromagnetic  Torque.     Elec.  W.  and  Eng.     Dec.  3,  1904. 

Alternating  Current  Commutator  Motors.  Trans.  Cornell  Elec.  Society. 
1904-05- 


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